This paper proposes a reinterpretation of the Chinese worldview on equilibrium/nonequilibrium and yin-yang in the context of science and draws the correlative aspects with irreversible thermodynamics and quantum reality, such as instability, nonlinearity, nonequilibrium, and temporality. The paper argues that Prigogine's expressions on dissipative structures and their role in thermodynamic systems far from equilibrium, complexity, and irreversibility resonate with the principles in Yijing. Instability, far-from-equilibrium, irreversibility, probability, bifurcation, and self-organisation are intrinsic properties of nature appearing at all levels. Information is (...) the basis of all changes. The agency of change is the human with a consciousness interpreting the information existing in the probability space between heaven and earth. The paper outlines a modelling approach with the self-organising human in the centre between heaven and earth, representing living systems as discrete dynamical systems presented with binary yin-yang choices. The concepts of yin-yang and information causality are central to Yijing’s understanding of change and are clarified in this paper. (shrink)

The sequential patterns of the sixty-four hexagrams in the Yijing, variously known as I Ching (the Book of Changes) are structured to embrace the universe of possibilities, scenarios and probabilities. Each hexagram equates to each moment in space-time. With the arrow of time, a string of hexagrams represent a string of moments. A probability curve can be formed from the string of hexagrams. Physicists call this mathematical entity a wave function which is constantly changing and proliferating. A wave function is (...) mathematical representation of all possibilities that can happen to an observed entity when it interacts with an observer. The form of the wave function can be calculated by the Schrodinger wave equation for any part of the range of moments. The string of hexagrams deal with probabilities. Physicists deal mainly with two wave forms and functions – dynamic wave that follows the Schrodinger wave equation and the second phenomenon is the “collapse of the wave function” which is abrupt and discontinuous. Which part of the wave collapses is a matter of probability and chance. The wave transition from the first to the second is call the quantum jump. This exhibited phenomenon is very similar to how the hexagram in the Yijing. When unobserved, the sequential formation of the hexagrams, moment by moment, form a probability wave but when it is observed, it abruptly collapses. It is the abrupt collapse of all the development aspects of the wave function except the one that actualizes and that particular hexagram is therefore the mathematical representation of the observed entity. What spurs all the changes is the energy that flows through the system and all the interacting waves are interconnected and interdependent and they form the energy fields. Emphasis is on the stringed hexagrams, each possesses a sophisticated mathematical structure, suggesting at the same time that it would hold great significance as an integral part of the whole of the wave or energy field. The subject of this paper is on the quantum- informational theoretical framework of Yijing. (shrink)

A gas relaxing into equilibrium is often taken to be a process in which a system moves from an “improbable” to a “probable” state. Given that the thermodynamic entropy increases during such a process, it is natural to conjecture that the thermodynamic entropy is a measure of the probability of a macrostate. For nonideal classical gases, however, I claim that there is no clear sense in which the thermodynamic entropy of a macrostate measures its probability. We must therefore reject the (...) idea that thermodynamic entropy and probability are connected in a deep and general way. (shrink)

In the quest and search for a physical theory of everything from the macroscopic large body matter to the microscopic elementary particles, with strange and weird concepts springing from quantum physics discovery, irreconcilable positions and inconvenient facts complicated physics – from Newtonian physics to quantum science, the question is- how do we close the gap? Indeed, there is a scientific and mathematical fireworks when the issue of quantum uncertainties and entanglements cannot be explained with classical physics. The Copenhagen interpretation is (...) an expression of few wise men on quantum physics that was largely formulated from 1925 to 1927 namely by Niels Bohr and Werner Heisenberg. From this point on, there is a divergence of quantum science into the realms of indeterminacy, complementarity and entanglement which are principles expounded in Yijing, an ancient Chinese knowledge constructed on symbols, with a vintage of at least 3 millennia, with broken and unbroken lines to form stacked 6-line structure called the hexagram. It is premised on probability development of the hexagram in a space-time continuum. The discovery of the quantization of action meant that quantum physics could not convincingly explain the principles of classical physics. This paper will draw the great departure from classical physics into the realm of probabilistic realities. The probabilistic nature and reality interpretation had a significant influence on Bohr’s line of thought. Apparently, Bohr realized that speaking of disturbance seemed to indicate that atomic objects were classical particles with definite inherent kinematic and dynamic properties (Hanson, 1959). Disturbances, energy excitation and entanglements are processual evolutionary phases in Yijing. This paper will explore the similarities in quantum physics and the methodological ways where Yijing is pivoted to interpret observable realities involving interactions which are uncontrollable and probabilistic and forms an inseparable unity due to the entanglement, superposition Transgressing disciplinary boundaries in the discussion of Yijing, originally from the Western Zhou period (1000-750 BC), over a period of warring states and the early imperial period (500-200 BC) which was compiled, transcribed and transformed into a cosmological texts with philosophical commentaries known as the “Ten Wings” and closely associated with Confucius (551- 479 BC) with the Copenhagen Interpretation (1925-1927) by the few wise men including Niel Bohr and Werner Heisensberg would seem like a subversive undertaking. Subversive as the interpretations from Yijing is based on wisdom derived from thousands of years from ancient China to recently discovered quantum concepts. The subversive undertaking does seem to violate the sanctuaries of accepted ways in looking at Yijing principles, classical physics and quantum science because of the fortified boundaries that have been erected between Yijing and the sciences. Subversive as this paper may be, it is an attempt to re-cast an ancient framework where indeterminism, complementarity, non-linearity entanglement, superposition and probability interpretation is seen in today quantum’s realities. (shrink)

The work in this paper is presented with this spirit to draw the relatedness of Yijing to quantum physics and seek to express the continuity between the ancient sages and contemporary scientific thought. Yijing is abstract philosophical and can provide an excellent method for generating, structuring and exploring quantum fields relevant to our present level of scientific knowledge. Further, the view of reality that science emphasizes as a seamless, continuous field is the same as Yijing where ‘self’ as particle is (...) deeply integrated into the basic fabric of reality through their consciousness. It is this consciousness that interacts and co-relates to that field of interconnectedness. (Schöter, 2011) The wholeness of realities, in Yijing, are layer of fields interacting, changing, extending into possibilities and uncertainties. (shrink)

Part I of the present work outlined the rigorous application of information theory to a quantum mechanical system in a thermodynamic equilibrium state. The general formula developed there for the best-guess density operator $\hat \rho$ was indeterminate because it involved in an essential way an unspecified prior probability distribution over the continuumD H of strong equilibrium density operators. In Part II mathematical evaluation of $\hat \rho$ is completed after an epistemological analysis which leads first to the discretization ofD H and (...) then to the adoption of a suitable indifference axiom to delimit the set of admissible prior distributions. Finally, quantal formulas for information-theoretic and thermodynamic entropies are contrasted, and the entire work is summarized. (shrink)

A new axiomatic treatment of equilibrium thermodynamics—thermostatics—is presented. The equilibrium states of a thermal system are assumed to be represented by a differentiable manifold of dimensionn + 1 (n finite). The empirical temperature is defined by the notion of thermal equilibrium. Empirical entropy is shown to exist for all systems with the property that the total work delivered along closed adiabats is zero. Absolute entropy and temperature follow from the additivity of heat and energy for two separate systems in thermal (...) equilibrium considered as a whole. The absolute temperature is defined up to a multiplicative constant. The exterior differentiable calculus of Cartan is introduced and in a subsequent paper its use for the derivation of standard results in thermostatics will be explained. (shrink)

This volume contains the invited lectures and a selection of the contributed papers and posters of the workshop on "Fluctuations and Sensitivity in Nonequil ibrium Systems", held at the Joe C. Thompson Conference Center, Un i vers ity of Texas at Austin, March 12-16, 1984. The workshop dealt with stochastic phenomena and sensi­ tivity in nonequilibrium systems from a macroscopic point of view. Durin9 the last few years it has been realized that the role of fluctuations is far less trivial (...) in systems far from equilibrium than in systems under thermodynamic equilibrium condi­ tions. It was found that random fluctuations often are a determining factor for the state adopted by macroscopic systems and cannot be regarded as secondary effects of minor importance. Further, nonequilibrium systems are also very sensitive to small systematic changes in their environment. The main aims of the workshop were: i) to provide scientists with an occasion to acquaint themselves with the state of the art in fluctuation theory and sensitivity analysis; ii) to provide a forum for the presentation of recent advances in theory and experiment; iii) to bring toge­ ther theoreticians and experimentalists in order to delineate the major open problems and to formulate strategies to tackle these problems. The organizing committee of the workshop consisted of W. Horsthemke, O. K. Konde­ pudi, G. Dewel, G. Nicolis, I. Prigogine and L. Reichl. (shrink)

This thesis makes the issue of reconciling the existence of thermodynamically irreversible processes with underlying reversible dynamics clear, so as to help explain what philosophers mean when they say that an aim of nonequilibrium statistical mechanics is to underpin aspects of thermodynamics. Many of the leading attempts to reconcile the existence of thermodynamically irreversible processes with underlying reversible dynamics proceed by way of discussions that attempt to underpin the following qualitative facts: (i) that isolated macroscopic systems that begin away from (...) equilibrium spontaneously approach equilibrium, and (ii) that they remain in equilibrium for incredibly long periods of time. These attempts standardly appeal to phase space considerations and notions of typicality. This thesis considers and evaluates leading typicality accounts, and, in particular, highlights their limitations. Importantly, these accounts do not underpin a large and important set of facts. They do not, for example, underpin facts about the rates in which systems approach equilibrium, or facts about the kinds of states they pass through on their way to equilibrium, or facts about fluctuation phenomena. To remedy these and other shortfalls, this thesis promotes an alternative, and arguably more important, line of research: understanding and accounting for the success of the techniques and equations physicists use to model the behaviour of systems that begin away from equilibrium. Accounting for their success would help underpin not just the qualitative facts the literature has focused on, but also many of the important quantitative facts that typicality accounts cannot. This thesis also takes steps in this promising direction. It outlines and examines a technique commonly used to model the behaviour of an interesting and important kind of system: a Brownian particle that's been introduced to an isolated homogeneous fluid at equilibrium. As this thesis highlights, the technique returns a wealth of quantitative and qualitative information. This thesis also attempts to account for the success of the model and technique, by identifying and grounding the technique's key assumptions. (shrink)

A unified axiomatic theory that embraces both mechanics and thermodynamics is presented in three parts. It is based on four postulates; three are taken from quantum mechanics, and the fourth is the new disclosure of the existence of quantum states that are stable (Part I). For nonequilibrium and equilibrium states, the theory provides general original results, such as the relation between irreducible density operators and the maximum work that can be extracted adiabatically (Part IIa). For stable equilibrium states, it shows (...) for the first time that the canonical and grand canonical distributions are the only stable distributions (Part IIb). The theory discloses the incompleteness of the equation of motion of quantum mechanics not only for irreversible processes but, more significantly, for reversible processes (Part IIb). It establishes the operational meaning of an irreducible density operator and irreducible dispersions associated with any state, and reveals the relationship between such dispersions and the second law (Part III). (shrink)

A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a pair of (...) observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results. (shrink)

In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we have addressed the mechanical foundations of equilibrium thermodynamics on the basis of the Generalized Helmholtz Theorem. It was found that the volume entropy provides a good mechanical analogue of thermodynamic entropy because it satisfies the heat theorem and it is an adiabatic invariant. This property explains the ``equal'' sign in Clausius principle ($S_f \geq S_i$) in a purely mechanical way and suggests that the volume entropy (...) might explain the ``larger than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations were considered. Based on the principles of microscopic (quantum or classical) mechanics here we prove that, provided the initial equilibrium satisfy the natural condition of decreasing ordering of probabilities, the expectation value of the volume entropy cannot decrease for arbitrary transformations performed by some external sources of work on a insulated system. This can be regarded as a rigorous quantum mechanical proof of the Second Law. We discuss how this result relates to the Minimal Work Principle and improves over previous attempts. The natural evolution of entropy is towards larger values because the natural state of matter is at positive temperature. Actually the Law of Entropy Decrease holds in artificially prepared negative temperature systems. (shrink)

Part II of this three-part paper presents some of the most important theorems that can be deduced from the four postulates of the unified theory discussed in Part I. In Part IIa, it is shown that the maximum energy that can be extracted adiabatically from any system in any state is solely a function of the density operator $\hat \rho$ associated with the state. Moreover, it is shown that for any state of a system, nonequilibrium, equilibrium or stable equilibrium, a (...) unique propertyS exists which is proportional to the total energy of the system minus the maximum energy that can be extracted adiabatically from the system in combination with a reservoir. For statistically independent systems, propertyS is extensive, it is invariant during all reversible processes, and it increases during all irreversible processes. (shrink)

The special composition question, which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, (...) the thermodynamic composition principle : Multiple systems in thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, might form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, “thermal contact” can be analyzed using the mereotopological predicate “self-connectedness”. Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected. (shrink)

The Tao Tê Ching is probably the world's second most translated and annotated book , yet it remains among the most enigmatic. Of its eighty-one chapters, no one denies that the most important is the first, and many scholars go further to claim that it is the key to the whole work: if it is understood fully, all the rest may be seen to be implied. Unfortunately, the first chapter also happens to be the most ambiguous. But even so, after (...) so much attention can there be anything left to say? It seems to me that an important point has been missed or at least obscured, and that the popularity of certain translations has made this obscuration more prevalent recently. To correct this, I shall offer below a line-by-line explication of this crucial passage. The following interpretation first demonstrates the parallel structure of the first eight lines as signifying two different ways of experiencing: lines one, three, five and seven refer to the experience of Tao, and lines two, four, six and eight to our more usual way of experiencing the world. I shall suggest that the difference between these ways is the difference between our familiar dualistic experience and a much less common nondualistic way of experiencing in which there is no bifurcation between subject and object. Second, we shall see that the parallel structure unfolds dialectically: each succeeding pair of lines elaborates upon the issues that naturally arise in response to the preceding pair. In the process of showing this, I shall take sides on the two main controversies over this chapter: first, whether it should be interpreted cosmologically or ontologically/epistemologically , and second, whether lines, five and six should be punctuated to translate yü as ‘desire/intention’. My main thesis is that the traditional understanding of yü as ‘desire’ or ‘intention’ is an essential part of the meaning of the chapter. This is by no means an original claim, but why it is so important does not seem to have been noticed before and provides the reason for this paper. Wing-tsit Chan's criticism of such translations, that ‘intention interrupts the thought of the chapter’, 1 is thus a serious misreading of the text. (shrink)

The conventional claims and concepts of 5* - 8* are a hang-over from the classical theory of thermodynamics – i.e. thermodynamics based on a fully deterministic micro-theory, developed in the time of Boltzmann, Loschmidt and Gibbs in the late C19th. The classical theory has well-known ‘reversibility paradoxes’ when applied to the universe as a whole. But the introduction of intrinsic probabilities in quantum mechanics, and its consequent time asymmetry, fundamentally changes the picture.

The themes of connectedness and continuity, which are also mathematical properties, have run like a red thread through the last fifty years of History and Theory, notably in the theory of the narration of action in history. In this essay I review various answers to the question of the driving force that motivates action and that propels a sequence, continuous or discontinuous. These answers underpin narrative strategies intended to solve the problem of human agency and thereby to provide the basis (...) for historical narratives. I argue that both continuous and discontinuous conceptions of history have to do with the restrictive concept of trajectory. Most of our familiar concepts such as trajectory, equilibrium, optimum, probability, and sensitivity to initial conditions are taken from mathematics and physics, but how well adapted are they to dealing with the time of actors, whose actions are intermingled with uncertainty? I shall present alternative concepts of dynamics, ones that no longer lead toward just one particular future or that reflect a single past. On this basis I suggest reorganizing our view of historical time along the principles of maintenance, acquisition, and victory. Historical sources trace back not to one story or one process that is plausible or that appeals to common sense, but to a whole family of processes. From the past, we can obtain sets of constraints that circumscribe sets of stories rather than a single scenario. I shall then propose a topology of the time of action based on my alternative conception of dynamics, a topology made of what I call viability kernels, capture basins, and victory domains. (shrink)

We consider work extraction from two finite reservoirs with constant heat capacity, when the thermodynamic coordinates of the process are not fully specified, i.e., are described by probabilities only. Incomplete information refers to both the specific value of the temperature as well as the label of the reservoir to which it is assigned. Based on the concept of inference, we characterize the reduced performance resulting from this lack of control. Indeed, the estimates for the average efficiency reveal that uncertainty regarding (...) the exact labels reduces the maximal expected efficiency below the Carnot value ), its minimum value reproducing the well known Curzon–Ahlborn value: \ . We also estimate the efficiency before the value of the temperature is revealed. It is found that if the labels are known with certainty, then in the near-equilibrium limit the efficiency scales as \ , while if there is maximal uncertainty in the labels, then the average estimate for efficiency drops to \ . We also suggest how the inferred properties of the incomplete model can be mapped onto a model with complete information but with an additional source of thermodynamic irreversibility. (shrink)

Using Schrödinger's generalized probability relations of quantum mechanics, it is possible to generate a canonical ensemble, the ensemble normally associated with thermodynamic equilibrium, by at least two methods, statistical mixing and subensemble selection, that do not involve thermodynamic equilibration. Thus the question arises as to whether an observer making measurements upon systems from a canonical ensemble can determine whether the systems were prepared by mixing, equilibration, or selection. Investigation of this issue exposes antinomies in quantum statistical thermodynamics. It is conjectured (...) that resolution of these paradoxes may involve a new law of motion in quantum dynamics. (shrink)

Many argue that the standard understanding of the second law of thermodynamics combined with the supposition, backed by recent scientific evidence, that the future is infinite entails that one is, most likely, a momentary Boltzmann brain that will quickly disintegrate into the cosmos. The argument is as follows: (1) Given infinite time, the universe will eventually reach thermodynamic equilibrium; (2) once there, every possible fluctuation away from equilibrium, no matter how improbable, will recur, ad infinitum; (3) those fluctuations that create (...) stable, long-lived creatures, such as we take ourselves to be, will be extremely rare compared to those that create short-lived brains that mistakenly think they are ordinary human beings; hence, by statistical reasoning, (4) one is, with overwhelming probability, just a fleeting instantiation of experience. I argue that this reasoning is invalid since it rests on an error regarding the relationship between infinite sets and their subsets. Once this error is eliminated, the power of the argument fades, and the evidence that we are ordinary human beings becomes decisive. Surprisingly, I find that the best argument for the Boltzmann brain hypothesis requires the assumption that the future is very long but finite. (shrink)

An introduction to the Yijing (I Ching) 易經 or Classic/Scripture of Change : its nature, its history of interpretation, and its cultural influences. New York: Oxford University Press (forthcoming).

I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; the central role of Hawking radiation in permitting (...) black holes to be in thermal contact with one another; the wide range of routes by which Hawking radiation can be derived and its back-reaction on the black hole calculated; the interpretation of Hawking radiation close to the black hole as a gravitationally bound thermal atmosphere. In an appendix I discuss recent criticisms of black hole thermodynamics by Dougherty and Callender. This paper confines its attention to the thermodynamics of black holes; a sequel will consider their statistical mechanics. (shrink)

The I Ching, probably the oldest book in existence, provides a system of knowledge that makes it possible to analyze the patterns of changes in life governed by the Immutable Law of Change. Whether we use the I Ching for divination or to study the principles involved with it, if we allow ourselves to be governed by its teachings, we shall enrich the content of our lives, free ourselves from anxiety, and become harmless or even intelligently helpful to others and (...) pleasant companions to ourselves. This translation of the I Ching has been especially prepared for practical use in divination. It is easier to use than any previous version, and the language is closer to that of the Chinese original. (shrink)

In his recent book, Time and Chance, David Albert claims that by positing that there is a uniform probability distribution defined, on the standard measure, over the space of microscopic states that are compatible with both the current macrocondition of the world, and with what he calls the “past hypothesis”, we can explain the time asymmetry of all of the thermodynamic behavior in the world. The principal purpose of this paper is to dispute this claim. I argue that Albert's proposal (...) fails in his stated goal—to show how to use the time‐reversible dynamics of Newtonian physics to “underwrite the actual content of our thermodynamic experience” (Albert 2000, 159). Albert's proposal can satisfactorily explain why the overall entropy of the universe as a whole is increasing, but it does not and cannot explain the increasing entropy of relatively small, relatively short‐lived systems in energetic isolation without making use of a principle that leads to reversibility objections. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:A Way of Music Education: Classic Chinese Wisdoms by C. Victor FungJui-Ching WangC. Victor Fung, A Way of Music Education: Classic Chinese Wisdoms (New York, Oxford University Press, 2018)The philosophical inquiry of music and music education has traditionally been limited to a Western lineage, primarily Greek civilization. Many prominent scholars of music education philosophy in the English-speaking world have long restricted their quests to the offspring of this (...) Western philosophy. Although music education scholars have urged a need for more than one "single philosophical foundation" for the field,1 not much has been done systematically to make up for this shortcoming until most recently when scholars such as Wayne Bowman, Ana Luciá Frega, Victor Fung, and Leonard Tan started to call for a more inclusive way of thinking to accommodate the "complexity, plurality, and change" in twenty-first century music education settings.2 To respond to this call, the primary contribution of A Way of Music Education: Classic Chinese Wisdoms is to provide an alternative for examining the phenomena of music teaching and learning by introducing classic Chinese philosophies, Yijing (the Book of Change), Confucianism, and Daoism to bridge the philosophical gap between the West and the East.This book is organized in three parts. Part I, Classical Chinese Philosophies and Music Educational Interpretations, consists of four chapters with the [End Page 116] fundamental background of each philosophy Fung adopts and its interpretation and application in music and music education. Part II, Complementarity and a Trilogy, contains four chapters that help explain how Yijing, Confucianism, and Daoism complement each other as a "harmonious triad," not only in their original context but also in the philosophical frame of contemporary music and music education. The two chapters in Part III, A New Way of Thinking and Practical Implications, discuss practical implications of these classic philosophical ideologies in music education. An epilogue calls for future research on more Chinese classics in both music education and other non-music fields as Fung believes that these rich classic wisdoms are transcendental in time and space, and thus can be experienced as a way of life that "champions the human spirit in relation to the ever-changing natural environment, material life, and social system."3 Lastly, to help readers unfamiliar with Chinese philosophy, a glossary defines the key Chinese terms in each chapter with original Chinese characters and English translations. In addition, flow charts and diagrams help readers visualize the application of complex classic Chinese principles to music education.Attempting to develop "a new way of thinking in music education,"4 Fung situates his inquiry in an "organismic worldview,"5 a way of examining oneself and his/her relation to all elements of the world, a common philosophical thread derived from ancient classic Chinese philosophies of Yijing, Confucianism, and Daoism. Transcending the long debate about the praxial philosophy and aesthetic philosophy of music education, Fung uses these Chinese philosophical principles to explain human musical behaviors first with an ontological lens. He then moves on to examine from a utilitarian perspective the significance of these musical behaviors as inseparable parts of the 'humanly human.' Carefully framing interpretations within the three Chinese classic philosophies, Fung uses a comparative method to scrutinize the meaning of music for human beings who practice it, to their social network (small or large), and to their natural environment. Fung's comparison of the similarities and differences of ancient Chinese principles concludes that "music and music education [are] part of the larger entities and phenomena that cut across time and space."6 Such comparison exemplifies the value of comparative philosophy in "acknowledging and appreciating differences in a realization of the complementarity of perspectives."7 As a result, Fung is able to complement ideas from the seeming contradiction between Confucianism's "human-centric" ideology and Daoism's "dao-centric" ideology to cleverly picture a more comprehensive way of music in education: because "these two schools are addressing different human needs…, they influence each other and provide momentum for each other."8Moreover, going beyond the "minor varieties of comparisons" within the Chinese classics, Fung challenges himself to a higher level of inquiry stretching [End Page 117] out to... (shrink)

We provide a 'verisimilitudinarian' analysis of the well-known Linda paradox or conjunction fallacy, i.e., the fact that most people judge the probability of the conjunctive statement "Linda is a bank teller and is active in the feminist movement" (B & F) as more probable than the isolated statement "Linda is a bank teller" (B), contrary to an uncontroversial principle of probability theory. The basic idea is that experimental participants may judge B & F a better hypothesis about Linda as compared (...) to B because they evaluate B & F as more verisimilar than B. In fact, the hypothesis "feminist bank teller", while less likely to be true than "bank teller", may well be a better approximation to the truth about Linda. (shrink)

Recently, the correspondence between the air track scenario and quantum database search algorithm was revealed. The conservation laws of linear momentum and nonlinear kinetic energy in the former case, which involve sequential elastic collisions, have their analogs in the latter case. Obviously, probability normalization combined with the Born rule serves as an analog for kinetic energy conservation. Here we explore the linear conservation laws in a generic quantum database search. Regarding the non-uniform distribution of the marked state, the uneven state (...) is initially prepared. In this way, the Grover diffusion operator results in a linear but nonphysical conservation law. On the other hand, in the CTC-assisted database search with the vast reduction of query complexity, the nonlinear instead of linear conservation laws are found. Finally, we conjecture that there are no conservation laws in the generalized Grover’s algorithm including the imaginary number i. (shrink)

A novel thermodynamic perspective on natural selection is presented. In the case that life continuity is optimized in an ideal system, where relatively constant and homogeneous selective pressures favour a given competing species, natural selection leads that system to a stationary state of maximum genotypic uniformity of life and maximum sustainable consumption of available energy by life (competitive equilibrium). Structurally and functionally, this optimizing tendency towards competitive equilibrium looks similar to the optimizing tendency towards thermodynamic equilibrium of classical thermodynamics (maximum (...) energetic uniformity and maximum degradation of available energy). The principle of competitive exclusion may thus be conceptually viewed as an ecological manifestation of the second law of (classical) thermodynamics. On the other hand, the novel thermodynamic perspective on natural selection is discussed with regard to the open and nonequilibrium system of nature, where selective pressures vary in space and time. In this case, natural selection can induce diversity instead of uniformity, though an optimizing tendendcy towards maximum sustainable consumption of resources (optimization of life continuity) always remains. Overall, it is concluded that the action of natural selection favours the maximization of the sustainable consumption of energy at the level of individual organism. (shrink)

Daniel R. Brooks and E. O. Wiley have proposed a theory of evolution in which fitness is merely a rate determining factor. Evolution is driven by non-equilibrium processes which increase the entropy and information content of species together. Evolution can occur without environmental selection, since increased complexity and organization result from the likely capture at the species level of random variations produced at the chemical level. Speciation can occur as the result of variation within the species which decreases the probability (...) of sharing genetic information. Critics of the Brooks-Wiley theory argue that they have abused terminology from information theory and t thermodynamics. In this paper I review the essentials of the theory, and give an account of hierarchical physical information systems within which the theory can be interpreted. I then show how the major conceptual objections can be answered. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

The materialist critics argue that insuperable difficulties are encountered by the hypothesis that immaterial mental events such as thinking can act in any way on material structures such as neurons of the cerebral cortex, as is diagrammed in Fig. 8. Such a presumed action is alleged to be incompatible with the conservation laws of physics, in particular of the First Law of Thermodynamics. This objection would certainly be sustained by 19th century physicists and by neuroscientists and philosophers who are still (...) ideologically in the physics of the 19th century, not recognizing the revolution wrought by quantum physicists in the 20th century. Unfortunately it is rare for a quantum physicist to dare an intrusion into the brain-mind problem. But in a recent book the quantum physicist Margenau (1984) makes a fundamental contribution. It is a remarkable transformation from 19th century physics to be told (p. 22): "that some fields, such as the probability field of quantum mechanics carry neither energy nor matter." He goes on (p. 96) to state: "In very complicated physical systems such as the brain, the neurons and sense organs, whose constituents are small enough to be governed by probabilistic quantum laws, the physical organ is always poised for a multitude of possible changes, each with a definite probability; if one change takes place that requires energy, or more or less energy than another, the intricate organism furnishes it automatically. Hence, even if the mind has anything to do with the change, that is if there is a mind-body interaction, the mind would not be called upon to furnish energy." In summary (p. 97) Margenau states that: "The mind may be regarded as a field in the accepted physical sense of the term. But it is a nonmaterial field; its closest analogue is perhaps a probability field. It cannot be compared with the simpler nonmaterial fields that require the presence of matter (e.g. gravity) nor does it necessarily have a definite position in space. And so far as present evidence goes it is not an energy field in any physical sense, nor is it required to contain energy in order to account for all known phenomena in which mind interacts with brain". In formulating more precisely the dualist hypothesis of mind-brain interaction, the initial statement is that the whole world of mental events (World 2) has an existence as autonomous as the world of matter-energy (World I ) (Fig. 1). The present interactionist hypothesis does not relate to these ontological problems, but merely to the mode of action of mental events on neural events, that is of the nature of the downward arrows across the frontier in Fig. 8. Following Margenau (1984) the hypothesis is that mind-brain interaction is analogous to a probability field of quantum mechanics, which has neither mass nor energy, yet can cause effective action at microsites. More specifically it is proposed that the mental concentration involved in intentions (Figs. 7, 8) or attention (Fig. 4) or planned thinking (Figs. 5, 6) can cause neural events by a process analogous to the probability fields of quantum mechanics. -/- We can ask: what neural events could be appropriate recipients for mental fields that are analogous to quantal probability fields? Already we may have the answer in recent discoveries on the nature of the synaptic mechanism whereby one nerve cell communicates with another. (shrink)

In this paper I examine Albert’s (2000) claim that the low entropy state of the early universe is sufficient to explain irreversible thermodynamic phenomena. In particular, I argue that conditionalising on the initial state of the universe does not have the explanatory power it is presumed to have. I present several arguments to the effect that Albert’s ‘past hypothesis’ alone cannot justify the belief in past non-equilibrium conditions or ground the veracity of records of the past.

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

Thermodynamics is the foundation of many of the topics of interest in the religion‐science dialogue. Here a nonmathematical outline of the principles of thermodynamics is presented, providing a historical and conceptually understandable development that can serve teachers from disciplines other than physics. The contributions of Gibbs to both classical and rational thermodynamics, emphasizing the importance of the ensemble in statistical mechanics, are discussed. The seminal ideas of Boltzmann on statistical mechanics are contrasted to those of Gibbs in a discussion of (...) the microscopic interpretation of the second law. The role of information theory is discussed, and the modern ideas of Prigogine and nonequilibrium are outlined in some detail with further reference to the second law. Implications for our interaction with God are considered. (shrink)

Relativistic Thermodynamics of equilibrium processes has remained a strange chapter in the history of modern physics. It was established by Planck in 1908 as a simple application of Einstein's special theory of relativity. Einstein himself made substantial contributions and its final product remained officially unchallenged until 1965. In 1952, however, at the end of his career, Einstein challenged the theory in his correspondence with von Laue. Many of his unpublished suggestions anticipated the major works in the debate of the 1960s. (...) The debate on the theory of RTD started in 1965 and lasted over a decade. In the end, no satisfactory solution was found even though every possible alternative seemed to have been entertained. Most participants contended that the choice among the alternatives was a matter of convention, depending on how one defines the basic quantities in RTD. ;This dissertation provides a critical study of the history of RTD and a philosophical investigation of its foundations. The first half is a critical study of the origin and the early development of RTD; which culminated in a detailed and, to my best knowledge, the first thorough discussion of the Einstein-von Laue correspondence. In the second half, after the complexity of the problem is described in chapter 5, a solution is found for the whole controversy based on Anderson's sharp insights on the different meanings of the relativity principles. Unless one can prove that pure thermodynamic quantities are geometrical objects, there is no need to look for the Lorentz-Transformations for those quantities; but they do not qualify as geometrical objects for they can only be defined in the rest frame of a system. ;This study also shows how profound the relativity principles are, how difficult it is to grasp their real meaning, and how physicists were led astray by paying too much attention to the formalism of a theory but too little to the soundness of the basic assumptions from which the theory derived. (shrink)

In this paper, I develop a naturalistic conception of evolutionary progress. I argue that the Waddingtonian notion of adaptability can be embedded meaningfully into a framework which views living things as nonequilibrium structures. This thermodynamic interpretation places great emphasis on the dynamics of environmental change, whereas the classical conceptions are based on equilibrium conceptions of the evolutionary process. What improves in evolution is the ability of living things to stay alive in increasingly heterogeneous environments.

Given the generic canonical probability in phase φ=exp[β(Ψ-H)], contact is traditionally made with phenomenological thermodynamics by comparing the identity δ〈φ〉=0 with the relationTδS=δU+δW, δ indicating an arbitrary infinitesimal variation of the thermodynamic coordinates and angular brackets ensemble means. This paper is concerned with the inverse problem of finding both the generic form of the phase functionw such thatS=〈w〉 and the explicit form φ=αexp[(F-H)/kT] of the canonical distribution on the basis of the requirement that the consequences of the phenomenological laws must (...) be safeguarded, i.e., the relations between the quantities which are their concomitants must also be satisfied by their statistical representatives. Given the generic statistical formalism and specifically thatU=〈H〉, δW=−〈δH〉, the problem is soluble, granted the following generic assumption: “the statistical representative of the entropy is the ensemble mean of a function which depends upon the phase through φ alone.”. (shrink)

This article studies the current US-China relationship using the dialectic ideas of I Ching. Firstly, the researcher introduces some basic theories of the topic. The dialectics of I Ching is based on the philosophy of Yin and Yang, on which the “unity of opposites” thought is built. The state of a “unity of opposites” relationship can be either equilibrium or disequilibrium. Secondly, the researcher analyses the status quo and trend of the US-China relationship, which is a pair of “unity of (...) opposites,” consulting Hexagram Kui (睽卦, kuigua), Hexagram Ge (革卦, gegua), and Hexagram Tong Ren (同人卦, tongrengua) in I Ching. Hexagram Kui explains the emergence, development, and intensification of the US-China contradictions, and finds out the crux of the problem between the two. Hexagram Ge analyzes and explains that the US-China relationship is on course for harmony and peace but requires a “revolution.” The “revolution” transforms the old ways China and the United States get along with each other, rather than aims to decouple or isolate either of the two countries. Instead, China and the United States should interweave to a larger extent. Hexagram Tong Ren advises putting the US-China relationship in the global context, under the principles of “harmony in diversity” and “seeking common ground whilst reserving differences.” It demands realistic approaches to the US-China contradictions, which will result in not only a new model of the US-China relationship but also global unity that can achieve peace and development in the world. This research is optimistic about the future of the US-China relationship. According to the dialectics of I Ching, the imbalanced “unity of opposites” will always move to balance. And the current imbalance between China and the United States can reveal and unravel the US-China contradictions. The US-China relationship will move from conflicts to harmony. (shrink)

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

The thermodynamic behavior is analyzed of a single classical charged particle in thermal equilibrium with classical electromagnetic thermal radiation, while electrostatically bound by a fixed charge distribution of opposite sign. A quasistatic displacement of this system in an applied electrostatic potential is investigated. Treating the system nonrelativistically, the change in internal energy, the work done, and the change in caloric entropy are all shown to be expressible in terms of averages involving the distribution of the position coordinates alone. A convenient (...) representation for the probability distribution is shown to be the ensemble average of the absolute square value of an expansion over the eigenstates of a Schrödinger-like equation, since the heat flow is shown to vanish for each hypothetical “state.” Subject to key assumptions highlighted here, the demand that the entropy be a function of state results in statistical averages in agreement with the form in quantum statistical mechanics. Examining the very low and very high temperature situations yields Planck's and Boltzmann's constants. The blackbody radiation spectrum is then deduced. From the viewpoint of the theory explored here, the method in quantum statistical mechanics of statistically counting the “states” at thermal equilibrium by using the energy eigenvalue structure, is simply a convenient counting scheme, rather than actually representing averages involving physically discrete energy states. (shrink)

Varieties of chemical and phase equilibria are controlled by the minimum Gibbs energy principle, according to which the Gibbs energy for a system will have the minimum value at any given temperature and pressure. It is understood that the minimum is with respect to all nonequilibrium states at the same temperature and pressure. The abstract relation between Gibbs energy and the equilibrium constant is deduced from fundamental laws of thermodynamics. However, actual use of this relation calls for the Gibbs energy (...) as a function of concentrations of the chemicals. Since thermodynamics is formulated without any reference to materials, how does one get that relation? This article provides the answer, and in the process shows that application of theory to experiments requires several intermediate layers where theory and experiment commingle. (shrink)

The general attributes of ecosystems are examined and a naturally occurring reference ecosystem is established, comparable with the isolated system of classical thermodynamics. Such an autonomous system with a stable, periodic input of energy is shown to assume certain structural characteristics that have an identifiable thermodynamic basis. Individual species tend to assume a state of least dissipation; this is most clearly evident in the dominant species (the species with the best integration of energy acquisition and conservation). It is concluded that (...) ecosystem structure results from the antagonistic interaction of two nearly equal forces. These forces have their origin in the Principle of Most Action (least dissipation or least entropy production) and the universal Principle of Least Action. Most action is contingent on the equipartitioning of the energy available, through uniform interaction of similar individuals. The trend to Least action is contingent on increased dissipation attained through increasing diversity and increasing complexity. These principles exhibit a basic asymmetry. Given the operation of these opposing principles over evolutionary time, it is argued that ecosystems originated in the vicinity of thermodynamic equilibrium through the resonant amplification of reversible fluctuations. On account of the basic asymmetry the system was able to evolve away from thermodynamic equilibrium provided that it remained within the vicinity of ergodynamic equilibrium (equilibrium maintained by internal work, where the opposing forces are equal and opposite).At the highest level of generalization there appear to be three principles operating: i) maximum association of free-energy and materials; ii) energy conservation (deceleration of the energy flow) through symmetric interaction and increased homogeneity; and iii) the principle of least action which induces acceleration of the energy flow through asymmetrical interaction. The opposition and asymmetry of the two forces give rise to natural selection and evolution. (shrink)

Abstract.Growing interest in the origin of life, the physical foundations of biological theory, and the evolution of animal social systems has led to increasing efforts to understand the processes by which elements or living systems at one level of organizational complexity combine to form stable systems of higher order. J. Bronowski saw the need to extend or reformulate evolutionary theory to deal with the hierarchy problem and to account for the evolution of systems of “stratified stability.” The hierarchy problem has (...) become a matter of great interest also in nonequilibrium thermodynamic theory.An effort is made here to develop an abstract, phenomenological model, based on the laws of thermodynamics, to account for the origin and hierarchical evolution of living systems. It is argued that the principle of minimum entropy production, developed by I. Prigogine, applies generally to all thermodynamic systems and processes and is implicit in an extended and more complete formulation of the second law of thermodynamics. From this are derived a thermodynamic criterion and a principle of thermodynamic selection governing the formation of stable systems of “elements” of various levels of organization. Thermodynamic selection gives rise to the creation of “elements” having increasingly “open” characteristic structures which may combine spontaneously to form “social” or crystalline systems capable of growing and reproducing themselves through processes of fissioning or budding. Such simple, self‐reproducing systems are capable of evolving by natural selection, which is seen to be a special case of the more general process of thermodynamic selection. The principle of natural selection, thus formulated, has the character of a fundamental physical law. Self‐reproducing systems with suitably open hereditary programs may combine to form stable social systems, which may grow and reproduce as a unit. In this way self‐reproducing systems of increasing hierarchical order, size, and organizational complexity may evolve through processes of thermodynamic (natural) selection. Some implications of this open‐ended model and opportunities for testing its empirical and theoretical utility are explored. (shrink)

Advances our understanding of the the Yijing (also known as the I Ching) by comparing and contrasting it to Western philosophy.

In The Primary Way, the distinguished scholar of Chinese philosophy Chung-ying Cheng synthesizes his lifetime of work on the Yijing, also known as the I Ching or Book of Changes--Back cover.

In The Structure of Biological Science I argued that the theory of natural selection is a statistical theory for reasons much like those which makes thermodynamics a statistical theory. In particular, the theory claims that fitness differences are large enough and the life span of species long enough for increases in average fitness always to appear in the long run; and this claim, I held, is of the same form as the statistical version of the second law of thermodynamics.For the (...) latter law also makes a claim about the long run, and its statistical character is due to this claim: thermodynamic systems must in the long run approach an equilibrium level of organization that maximizes entropy. Over finite times, given local boundary conditions, an isolated mechanical system, like the molecules in a container of gas, may sometimes interact so as to move the entropy of the system further from, instead of closer to the equilbrium level. But given enough interacting bodies, and enough time, the system will always eventually move in the direction prescribed by the law. Thus, we can attach much higher probabilities to the prediction that non-equilibrium systems will reflect greater entropy in future periods than we can to predictions that they will move in the opposite direction. And as we increase the amount of time and the number of bodies interacting, the strength of the probability we can attach to the prediction becomes greater and greater. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, and Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)