The fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels–Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels–Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincare systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)

Proponents of two axioms of biological evolutionary theory have attempted to find justification by reference to nonequilibrium thermodynamics. One states that biological systems and their evolutionary diversification are physically improbable states and transitions, resulting from a selective process; the other asserts that there is an historically constrained inherent directionality in evolutionary dynamics, independent of natural selection, which exerts a self-organizing influence. The first, the Axiom of Improbability, is shown to be nonhistorical and thus, for a theory of change through (...) time, acausal. Its perception of the improbability of living states is at least partially an artifact of closed system thinking. The second, the Axiom of Historically Determined Inherent Directionality, is supported evidentially and has an explicit historical component. Historically constrained dynamic populations are inherently nonequilibrium systems. It is argued that living, evolving systems, when considered to be historically constrained nonequilibrium systems, do not appear improbable at all. Thus, the two axioms are not compatible. Instead, the Axiom of Improbability is considered to result from an unjustified attempt to extend the contingent proximal actions of natural selection into the area of historical, causal explanations. It is thus denied axiomatic status, and the effects of natural selection are subsumed as an additional level of constraint in an evolutionary theory derived from the Axiom of Historically Determined Inherent Directionality. (shrink)

Markov blankets – statistical independences between system and environment – have become popular to describe the boundaries of living systems under Bayesian views of cognition. The intuition behind Markov blankets originates from considering acyclic, atemporal networks. In contrast, living systems display recurrent, nonequilibrium interactions that generate pervasive couplings between system and environment, making Markov blankets highly unusual and restricted to particular cases.

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)

This second part of a two-part essay discusses recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their similarity transformation approach (see Part I), but the contemporary approach utilizes rigged Hilbert space (whereas the older approach used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, the use of similarity transformations shifts to the background. In its place arose an interest in the physical features of large Poincaré (...) systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)

This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special (...) feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of ) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis", which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4, and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided. (shrink)

We give an explicit solution of a model Boltzmann kinetic equation describing a gas between two walls maintained at different temperatures. In the model, which is essentially one-dimensional, there is a probability for collisions to reverse the velocities of particles traveling in opposite directions. Particle number and speeds (but not momentum) are collision invariants. The solution, which depends on the stochastic collision kernels at the walls, has a linear density profile and the energy flux satisfies Fourier's law.

The work in progress reported by Wright & Liley shows great promise, primarily because of their experimental and simulation paradigms. However, their tentative conclusion that macroscopic neocortex may be considered (approximately) a linear near-equilibrium system is premature and does not correspond to tentative conclusions drawn from other studies of neocortex.

The fundamental problem on which Ilya Prigogine and the Brussels- Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of (...) time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincar´. (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)

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)

The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon and to develop a mathematical formalism that can describe this direction as being due to the dynamics of physical systems. In part I of this essay, I review and assess an attempt to carry out an approach that received much of their attention from the early 1970s to the mid 1980s. In part II, I will discuss their more recent approach using rigged Hilbert spaces. (shrink)

Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is studied as an analytically tractable example, and a kinetic theory is formulated for describing the states of the particle. What is peculiar here is that the (inverse) temperature is treated as a dynamical variable. Dynamical hierarchy is introduced in conformity with the adiabatic scheme. Then, a (...) new analytical method is developed to show how the Fokker–Planck equation admits as a stationary solution the Maxwellian distribution modulated by the temperature fluctuations, the distribution of which turns out to be determined by the drift term. A careful comment is also made on so-called superstatistics. (shrink)

The article explores a set of issues determining the synergetics of artificial cognitive systems: conditions for the realization of non-equilibrium stability of systems, synthesis options of artificial cognitive system, as well as mechanisms of self-organization of consciousness formed on its basis. Artificial cognitive systems are proposed to include not only artificial intelligence systems imitating human thinking, but any multilevel systems that perform the functions of recognizing and remembering information, decision-making, storage, explanation, understanding and production of new knowledge. The defining property (...) of a cognitive system is the ability to make decisions. It is shown that the content of the cognitive system is consciousness, interpreted within the framework of the information concept as an information environment in which the extended model of reality is realized. Consciousness can be qualified as an open dynamic system. The state of such systems is determined by the processes occurring in them (thought processes – in the case of consciousness). For such systems, called "living", there is a realization of mechanisms of stable disequilibrium. The implementation of an artificial cognitive system is technically carried out on the basis of an artificial neural network, and organizationally – according to the actor or reactor model. Self-organization processes determining the synergetics of consciousness are a special case of the extreme principle, which is a consequence of the law of excessive reaction of supersystems, regulating the existence of dissipative systems at the expense of supersystem resources. The initiation of self-organization of consciousness is carried out by the process of thinking, which, due to the non-equilibrium stability of consciousness, does not stop. Thus thinking can be interpreted as a process of varying system parameters in search of suitable ones for extended modeling of reality. (shrink)

The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be defined unambiguously, but it is the time derivative or entropy production that governs ongoing processes in these systems. The differences in physical interpretation and thermodynamic role of entropy in equilibrium and nonequilibrium systems is emphasized and the observable aspects of entropy (...) production are noted. A basis for nonequilibrium thermodynamics is also outlined. (shrink)

The results of two recent articles expanding the Gibbs variational principle to encompass all of statistical mechanics, in which the role of external sources is made explicit, are utilized to further explicate the theory. Representative applications to nonequilibrium thermodynamics and hydrodynamics are presented, describing several fundamental processes, including hydrodynamic fluctuations. A coherent description of macroscopic relaxation dynamics is provided, along with an exemplary demonstration of the approach to equilibrium in a simple fluid.

This essay is an appreciative engagement with Karl Peters's Dancing with the Sacred (2002). Peters achieves a naturalistic theology of great power. Two themes are covered here. The first is how Peters gives ontological footing for a naturalistic conception of God conceived as the process of creativity in nature. Peters achieves this by conceiving creativity in terms of Darwinian random variation and natural selection combined with the notion of nonequilibrium thermodynamics. He gives ontological reference for a conception of God (...) similar to Henry Nelson Wieman's idea of creative transformation. The second theme is how Peters succeeds in translating this nonpersonal conception of God into a powerful view of naturalistic religion that can shape a religious form of life. The key is that Peters's God can be understood as present in experience. Peters provides naturalistic interpretations of grace and the cruciform structure of creativity; the latter addresses the problem of evil in a nuanced fashion. I conclude with three critical comments about Peters's environmental ethics, his use of the notion of mystery, and his failure to have a robust conception of human fault or sin. (shrink)

This paper develops analogies concerning the evolution of dissipative structures in nonequilibrium thermodynamics to interpret irrational human behavior in which one finds a lack of correspondence between the invested means and the consequences observed. In an attempt to positively explain the process of cooperation between the free human person and interacting God, I use philosophical categories of Whitehead's process philosophy in an aesthetic model that opposes composition and performance in a musical symphony. Certainly, the essence of human freedom can (...) be expressed in neither thermodynamical nor aesthetic terms. The models proposed can, however, facilitate our understanding of the mutual relations between God's action in the world and the drama of human free choice of moral evil. (shrink)

In the previous papers, it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy, subject to the constraint given by the Liouville equation averaged over the phase space, leads to a definition of the rate of entropy change for closed Hamiltonian systems without any additional assumptions. Here, we generalize this basic model and, with the introduction of the additional constraints which are equivalent to the hydrodynamic continuity equations, show that the results obtained are (...) consistent with the known results from the nonequilibrium statistical mechanics and thermodynamics of irreversible processes. In this way, as a part of the approach developed in this paper, the rate of entropy change and entropy production density for the classical Hamiltonian fluid are obtained. The results obtained suggest the general applicability of the foundational principles of predictive statistical mechanics and their importance for the theory of irreversibility. (shrink)

Unexpected discoveries in nonequilibrium physics and nonlinear dynamics are changing our understanding of complex phenomena. Recent research has revealed fundamental new properties of matter in far-from-equilibrium conditions, and the prevalence of instability-where small changes in initial conditions may lead to amplified effects.

The free energy principle says that any self-organising system that is at nonequilibrium steady-state with its environment must minimize its free energy. It is proposed as a grand unifying principle for cognitive science and biology. The principle can appear cryptic, esoteric, too ambitious, and unfalsifiable—suggesting it would be best to suspend any belief in the principle, and instead focus on individual, more concrete and falsifiable ‘process theories’ for particular biological processes and phenomena like perception, decision and action. Here, I (...) explain the free energy principle, and I argue that it is best understood as offering a conceptual and mathematical analysis of the concept of existence of self-organising systems. This analysis offers a new type of solution to long-standing problems in neurobiology, cognitive science, machine learning and philosophy concerning the possibility of normatively constrained, self-supervised learning and inference. The principle can therefore uniquely serve as a regulatory principle for process theories, to ensure that process theories conforming to it enable self-supervision. This is, at least for those who believe self-supervision is a foundational explanatory task, good reason to believe the free energy principle. (shrink)

There are two theoretical approaches in statistical mechanics, one associated with Boltzmann and the other with Gibbs. The theoretical apparatus of the two approaches offer distinct descriptions of the same physical system with no obvious way to translate the concepts of one formalism into those of the other. This raises the question of the status of one approach vis-à-vis the other. We answer this question by arguing that the Boltzmannian approach is a fundamental theory while Gibbsian statistical mechanics is an (...) effective theory, and we describe circumstances under which Gibbsian calculations coincide with the Boltzmannian results. We then point out that regarding GSM as an effective theory has important repercussions for a number of projects, in particular attempts to turn GSM into a nonequilibrium theory. (shrink)

A common strategy for simplifying complex systems involves partitioning them into subsystems whose behaviors are roughly independent of one another at shorter timescales. Dynamic causal models clarify how doing so reveals a system’s nonequilibrium causal relationships. Here I use these models to elucidate the idealizations and abstractions involved in representing a system at a timescale. The models reveal that key features of causal representations—such as which variables are exogenous—may vary with the timescale at which a system is considered. This (...) has implications for debates regarding which systems can be represented causally. (shrink)

Based on Newton’s laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed universe oscillating in phase-space. We find that the behavior of this universe as a whole can be represented by a free entropic oscillator whose lifespan is nonhomogeneous, thus implying that time is shorter or longer according to the state of this universe given through its entropy. We conclude that time reduces to the entropy production of (...) this universe and that a nonzero entropy production means that local fluctuations could exist giving rise to the appearance of masses and to the curvature of the space. (shrink)

Context: A central motivation behind various embodied, extended, and enactive (4E) approaches to cognition is to ground our understanding of minds and cognition within the biological structures that give rise to life. Because of this, their advocates often claim a natural kinship with dynamical and developmental systems theories. However, these accounts also explicitly or implicitly privilege individual organisms in ways that contrast with many of the insights of systems and developmental systems approaches to biology. Problem: The prioritization of individual organisms (...) within 4E approaches to cognition contrasts with the default entangled structure of biological systems associated with cognitive agency. We provide means for 4E cognitive science to move beyond an individual-centred view of cognitive agency. Method: We first identify and problematize individual-centredness within various predominant 4E approaches by comparison with biological research and developmental systems theory. Subsequently, we offer conceptual resources from the field of ecological research for understanding cognitive agency beyond the predominant focus on individual organisms. Results: Cognitive agency may be understood without privileging individual organisms by reading nonequilibrium maintenance in terms of a dynamic differentiation instead of individual organismic autonomy. This form of organizational structure corresponds to the notion of sympoiesis from ecological research. Implications: Approaching cognitive agency without privileging individual organisms should be invaluable to advocates of 4E cognition seeking to ground notions of cognition and mind within contemporary biological research. Constructivist content: We seek to expand upon existing constructivist perspectives on the organizing principles of cognitive agency, such as sensorimotor embodiment and autopoiesis, arguing that meta-organismic cognitive agents (including humans) embody distributed relations beyond the privileging of individual organisms. Key words: 4E cognition, autopoiesis, cognitive agency, developmental systems theory, enactivism, extended mind thesis, holobionts, sympoeisis. (shrink)

Many attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the dissipative approach to QFT, a new alternative formulation of the theory explaining the phenomena of particle creation and annihilation starting from nonequilibrium thermodynamics. It is shown that DQFT presents a rigorous mathematical structure, and a clear particle ontology, taking the best from the mentioned perspectives. Finally, after (...) the discussion of its principal implications and consequences, we compare it with the main Bohmian QFTs implementing a particle ontology. (shrink)

A simple molecular system is described consisting of the reciprocal linkage between an autocatalytic cycle and a self-assembling encapsulation process where the molecular constituents for the capsule are products of the autocatalysis. In a molecular environment sufficiently rich in the substrates, capsule growth will also occur with high predictability. Growth to closure will be most probable in the vicinity of the most prolific autocatalysis and will thus tend to spontaneously enclose supportive catalysts within the capsule interior. If subsequently disrupted in (...) the presence of new substrates, the released components will initiate production of additional catalytic and capsule components that will spontaneously re-assemble into one or more autocell replicas, thereby reconstituting and sometimes reproducing the original. In a diverse molecular environment, cycles of disruption and enclosure will cause auto-cells to incidentally encapsulate other molecules as well as reactive substrates. To the extent that any captured molecule can be incorporated into the autocatalytic process by virtue of structural degeneracy of the catalytic binding sites, the altered autocell will incorporate the new type of component into subsequent replications. Such altered autocells will be progenitors of “lineages” with variant characteristics that will differentially propagate with respect to the availability of commonly required substrates. Autocells are susceptible to a limited form of evolution, capable of leading to more efficient, more environmentally fitted, and more complex forms. This provides a simple demonstration of the plausibility of open-ended reproduction and evolvability without self-replicating template molecules or maintenance of persistent nonequilibrium chemistry. This model identifies an intermediate domain between prebiotic and biotic systems and bridges the gap from nonequilibrium thermodynamics to life. (shrink)

Life history theory predicts that greater extrinsic mortality will lead to earlier and higher fertility. To test this prediction, I examine the relationship between life expectancy at birth and several proxies for life history traits (ages at first sex and first marriage, total fertility rate, and ideal number of children), measured for both men and women. Data on sexual behaviors come from the Demographic and Health Surveys (DHS). Two separate samples are analyzed: a cross-sectional sample of 62 countries and a (...) panel sample that includes multiple cross-sectional panels from 48 countries. Multivariate regression analysis is used to control for potential confounding variables. The results provide only partial support for the predictions, with greater support among women than men. However, the prediction is not supported in sub-Saharan African countries, most likely owing to the nonequilibrium conditions observed in sub-Saharan Africa with respect to life expectancy. The applicability of the model to understanding HIV/AIDS risk behaviors is discussed. (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)

We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie–Bohm pilot-wave formulation of quantum physics, we argue that there is no Born rule at the fundamental level of quantum gravity with a non-normalisable Wheeler–DeWitt wave functional \(\Psi\). Instead the universe is in a perpetual state of quantum nonequilibrium with a probability density \(P\ne \left| \Psi \right| ^{2}\). Dynamical relaxation to (...) the Born rule can occur only after the early universe has emerged into a semiclassical or Schrödinger approximation, with a time-dependent and normalisable wave functional \(\psi\), for non-gravitational systems on a classical spacetime background. In that regime the probability density \(\rho\) can relax towards \(\left| \psi \right| ^{2}\) (on a coarse-grained level). Thus the pilot-wave theory of gravitation supports the hypothesis of primordial quantum nonequilibrium, with relaxation to the Born rule taking place soon after the big bang. We also show that quantum-gravitational corrections to the Schrödinger approximation allow quantum nonequilibrium \(\rho \ne \left| \psi \right| ^{2}\) to be created from a prior equilibrium ( \(\rho =\left| \psi \right| ^{2}\) ) state. Such effects are very tiny and difficult to observe in practice. (shrink)

Science, and with it our understanding of evolutionary processes, is itself undergoing evolution. The evolutionary framework still most frequently used by the general public to describe and guide processes of societal development is erroneously grounded in Darwinian perspectives or, at the very least, draws facile analogies from biological evolution. The present inquiry incorporates fresh insights on the general systemic nature of developmental dynamics from the most recent advances in the transdisciplinary realm of the sciences of complexity (e.g., general evolution theory, (...) cybernetics, information and communication theory, chaos theory, dynamical systems theory, and nonequilibrium thermodynamics). The description of the evolutionary trajectory of complex dynamical systems as irreversible, periodically chaotic, and strongly nonlinear agrees with certain features of the historical processes of societal development. But there are additional features of the evolutionary dynamic of natural systems that are seldom portrayed as part of human developmental deportment. These features include elements such as the convergence of existing systems at progressively higher levels of organization, the increasingly efficient utilization of environmental energy, and the complexification of system structures in states that are progressively further removed from chemical and thermodynamic equilibria. The sciences of complexity offer insight into the laws and dynamics that govern the evolution of complex systems across a variety of disciplinary areas of investigation. Through a study of the isomorphisms across disciplinary constructs in the theoretical analyses of the principles governing the evolution of human societies, it is possible to enrich the account of developmental dynamics at the socio-civilizational level. Such an account would further our understanding of the phenomenon of societal development and provide the means for the purposeful guidance of this phenomenon in accordance with general evolutionary principles. This article sets forth the type of considerations, and outlines a general research agenda, for inquiry toward an operational model of the evolutionary development of social systems. (shrink)

The emergence of macroscopic variables can be effected through coarse graining. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced in (...) the coarse graining, we do not provide a unique prescription. Most significantly, the grains, and by implication entropy, are only defined modulo a characteristic time scale of observation. (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)

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)

A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used (...) to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann’s principle of classical statistical thermodynamics. A new expression for a general nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics. (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.

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 scope of the thermodynamic theory of nonlinear irreversible processes is widened to include the nonlinear stability analysis of system motion. The emphasis is shifted from the analysis of instantaneous energy flows to that of the average work performed by periodic nonlinear processes. The principle of virtual work separates dissipative and conservative forces. The vanishing of the work of conservative forces determines the natural period of oscillation. Stability is then determined by the variations of the dissipative forces with amplitude of (...) oscillation. If the work is a minimum, under certain conditions, the motion is stable. Reduction to linear analysis shows the coincidence with the impedance analysis of electrical circuit theory. The theory is applied to the analysis of temporal interactions of nonlinear irreversible processes in the particular cases of synchronization and hysteresis. Characteristic nonequilibrium phenomena of directional energy transfers, self-excitation, system passivity, wave modulation, and “beat” phenomena are observed. Possible relationships with biological processes are discussed. (shrink)

Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather (...) than on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert’s time-dependent projection operator formalism. This allows to better understand how general proposals for understanding probability in statistical mechanics, namely quantum approaches and almost-objective probabilities, can be accomodated in the MZ formalism. Moreover, I will provide a detailed physical analysis, based on the MZ formalism, of various proposals from the philosophical literature, such as Robertson’s theory of justifying coarse-graining via autonomous macrodynamics, Myrvold’s problem of explaining autonomous macrodynamics, and Wallace’s simple dynamical conjecture. (shrink)

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)

We consider the relativistic statistical mechanics of an ensemble of N events with motion in space-time parametrized by an invariant “historical time” τ. We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses to find approximate dynamical equations for the kinetic state of any nonequilibrium system, to the relativistic case, and obtain a manifestly covariant Boltzmann- type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This (...) equation is then used to prove the H-theorem for evolution in τ. In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential V(q), where q is an invariant distance in the Minkowski space-time. The two- body correlations are taken to have the support in a relative O(2, 1)-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit. (shrink)

Thermodynamic implications of anisotropic gas-surface interactions in a closed molecular flow cavity are examined. Anisotropy at the microscopic scale, such as might be caused by reduced-dimensionality surfaces, is shown to lead to reversibility at the macroscopic scale. The possibility of a self-sustaining nonequilibrium stationary state induced by surface anisotropy is demonstrated that simultaneously satisfies flux balance, conservation of momentum, and conservation of energy. Conversely, it is also shown that the second law of thermodynamics prohibits anisotropic gas-surface interactions in “equilibrium”, (...) even for reduced dimensionality surfaces. This is particularly startling because reduced dimensionality surfaces are known to exhibit a plethora of anisotropic properties. That gas-surface interactions would be excluded from these anisotropic properties is completely counterintuitive from a causality perspective. These results provide intriguing insights into the second law of thermodynamics and its relation to gas-surface interaction physics. (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 extension of quantum mechanics to a general functional space (“rigged Hilbert space”), which incorporates time-symmetry breaking, is applied to construct extract dynamical models of entropy production and entropy flow. They are illustrated by using a simple conservative Hamiltonian system for multilevel atoms coupled to a time-dependent external force. The external force destroys the monotonicity of the ℋ-function evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around the (...) unstable particles. (shrink)

We considered peculiarities of the evolution of a region with sharp boundaries that is filled with a partially ionized plasma and is a part of the volume of a condensed target. The creation of such a region in the near-surface layer of the target can be related to the action of an external impulse symmetric ionizator or to the action of an intense small-extension shock wave on the target surface. We defined the conditions such that their fulfilment during the establishment (...) of the equilibrium between the Coulomb attraction of electrons and ions with atom ionization multiplicity Z* 1 and the kinetic pressure of electrons causes both the compression of this region and its ionization to the state with Z* 2 > Z* 1. The last leads to a further additional compression and ionization. Under these conditions, the spontaneous avalanche-like ionization of atoms of the target to the state of ‘‘bare’’ nuclei occurs synchronously with the avalanche-like metallization and the self-compression of the target. We showed that the avalanche-like ionization and the self-compression of the target happen in the case where the gas of degenerate electrons has drift momentum. If the region with initial ionization has the form of thin spherical layer, the process of avalanche-like ionization and self-compression of the target in this region is accompanied by the accelerated movement of the plasma layer to the target center. One of the reasons for the accelerated movement is the surface tension in a bounded domain of the nonequilibrium plasma layer neutralized by ions of the target. With increase in the velocity of movement of this layer to the target center, the additional self-compression of the system of electrons and nuclei to the state of degenerate electron gas occurs. At the leading edge of the running layer with extremely high electron density which is neutralized by nuclei of the target, the formation of a collapse of the electron--nucleus system proceeds, and the binding energy maximum for the electron--nucleus system shifts from A≈60 to A ≫ 60. This result makes possible the fast synthesis of superheavy nuclei. The decay of the collapse state, a partial restoration of the target structure, its rapid cooling, and the condensation of a part of the products of nuclear reactions happen in the target volume at the trailing edge of the moving plasma layer. Upon such a scanning propagation of the wave with high electron density, all the target substance is involved, step-by-step, to the process of nuclear transformations. At the target center, the moving plasma layer is squeezed with the formation of the state of quasistationary collapse under inertial confinement. Then the collapse state decays irreversibly. (shrink)