The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a (...) book and several articles, quoted throughout. (shrink)

The Anthropocene crisis is frequently described as the rarefaction of resources or resources per capita. However, both energy and minerals correspond to fundamentally conserved quantities from the perspective of physics. A specific concept is required to understand the rarefaction of available resources. This concept, entropy, pertains to energy and matter configurations and not just to their sheer amount. However, the physics concept of entropy is insufficient to understand biological and social organizations. Biological phenomena display both historicity and systemic (...) properties. A biological organization, the ability of a specific living being to last over time, results from history, expresses itself by systemic properties, and may require generating novelties The concept of anti-entropy stems from the combination of these features. We propose that Anthropocene changes disrupt biological organizations by randomizing them, that is, decreasing anti-entropy. Moreover, second-order disruptions correspond to the decline of the ability to produce functional novelties, that is, to produce anti-entropy. (shrink)

n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity (...) along evolution. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness. (shrink)

Ce livre part d'un constat - la tutelle du réductionnisme issu du cognitivisme (années 1960-1970) - et du désir d'affirmer une complexité scientifique, philosophique et artistique, via la théorie des systèmes dynamiques. Deux parties d'abord. L'une philosophique : unité de la conscience et problème des attentats à l'aune leibnizienne ; l'autre artistique : installations sonores et visuelles, mouvements horizontaux, question du Je et de l'altérité, images composites (vidéo et cinéma expérimental), espaces topologiques cinématographiques et musique dans ses rapports avec le (...) cerveau. Après un historique des systèmes dynamiques, la part scientifique traite, elle, de neurosciences non-linéaires, de biodynamique, de mesure de la complexité et de l'(anti-)entropie dans l'ontogenèse. En une vue transversale, ce livre opte pour une "métadisplinarité" et défend un cognitivisme non-linéaire. (shrink)

An indifference principle says that your credences should be distributed uniformly over each of the possibilities you recognise. A chance deference principle says that your credences should be aligned with the chances. My thesis is that, if we are anti-Humeans about chance, then these two principles are incompatible. Anti-Humeans think that it is possible for the actual frequencies to depart from the chances. So long as you recognise possibilities like this, you cannot both spread your credences evenly and (...) defer to the chances. I discuss some weaker forms of indifference which will allow anti-Humeans to defer to the chances. (shrink)

This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, (...) in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field. (shrink)

Why is there something rather than nothing? This question, formulated by Leibniz, constitutes the basis of modern European ontology. In many ways this can be termed the main question of philosophy; but if so, a similar but less attended to question comes to mind, which I shall call the second best question of philosophy. The second best question of philosophy: Why is it better that there is something rather than nothing? seems to constitute a natural basis for moral theory. The (...) latter question often appears in philosophy of religion, in arguments leading to the thesis that God the Creator is good. Yet, modern moral philosophy tended to shy away from such a direct grounding in metaphysics. Not anymore. Luciano Floridi’s ethics based on anti-entropy is still a new and somewhat understated theory; having originated from information ethics it seems to have a hard time establishing itself as a general moral theory. But the potential of becoming a major alternative to the main positions in moral theory is there. It is my goal in this paper to highlight the promise, as well as certain difficulties, of Floridi’s theory. I will also undertake to move the work on anti-entropy ethics one step further, towards becoming a general moral theory. (shrink)

Big History - an integral conception of the past since the Big Bang until today - is a novel subject of cross-disciplinary interest. The concept was construed in the 1980-1990s simultaneously in different countries, after relevant premises had matured in the sciences and humanities. Various versions and traditions of Big History are considered in the article. Particularly, most of the Western authors emphasize the idea of equilibrium, and thus reduce cosmic, biological, and social evolution to the mass-energy processes; the informational (...) parameter involving all mental and spiritual aspects are seen as epiphenomena of material structures' complication that do not play their own role in evolution. In Russian tradition ascending to A. Bogdanov, E. Bauer, I. Prigogine, and E. Jantsch, sustainable non-equilibrium patterns are used. This implies attention to the pan-material sources and evolution of mental capacities and spiritual culture (as basic anti-entropy instruments) and humans' growing intervention in the material processes on Earth and outside it. The non-equilibrium approach in the context of modern control and self-organization theories, alters the portrayal of the past, and still more dramatically, estimation of the civilization's potential perspectives. (shrink)

The entropic state that engulfed the East Coast of Australia in the first eight months of 2020 followed thirty years of uninterrupted economic growth and 10 years of tenuous federal governments divided on the question of climate change. The twin geophysical crises of catastrophic bushfires and the COVID-19 pandemic have led to a public reckoning around our guardianship of the environment, as well as our relationship with science and indigenous knowledge. Congruent with this was the rapid transformation of both schools (...) and universities to online learning, causing the most significant rupture to the traditional ‘grammar of schooling’ for decades. This unprecedented conflation of crises has resulted in the unusual situation where education can be radically transformed, as the material conditions that usually remain latent (thus negating the possibility for change) suddenly exist. As a result, there has been an increased openness to pedagogies of potentiality, as schools and universities resist the urge to ‘return to normal’. Amongst these pedagogies, the philosophy of Bernard Stiegler is unique in its direct response to the entropic state with a counter-impulse, negantropy, which seeks to harness our technological capacity under an ethos of care and unite it with our existential purpose to flourish and thrive. This paper will consider the possibilities of Stiegler’s utopian call for action in relation to the Australian context, as schools and universities reconceptualise the sharing of knowledge and the purpose of education that seeks to rectify the gaps of the past. (shrink)

The conceptual gambit of this article is to propose that the notion of anti-entropy should be complemented by that of exergy investment or destruction, a term first proposed by Zoran Rant in 1956. It argues that one of Bernard Stiegler’s most important interventions into deconstruction is the thermodynamic reformulation of Derridean différance. I argue that we should view the idea of anti-entropy as likewise the displacement of entropy to an external system. With the notion of (...) exergy, it becomes possible to outline an economics of exergy expenditure and investment that considers this displacement. Having argued for the necessity of exergy as a concept that may complement anti-entropy, I demonstrate that this economy of exergy expenditure, through transductive analogy, can be applied to signification. An economics of exergy may give crucial insight into the transcendental problem of signification; that which Derrida’s notion of différance first responded to. I ask the question: can a trace-like logic of sense be understood energetically if trace itself is understood to be materially inscribed into the world? Having explored this question, I then outline how education might be understood as both the means through with traditional significations are energetically maintained as well as the means through which metastable significations can be disrupted. I use the recent banning of anti-capitalist literature in the UK as an example of what I call logomachics, a conflict of significative exergetic investment and disinvestment. (shrink)

In the art of radical Informel, we encounter works with emphasised non-pictoriality, non-semantics and non-referentiality, as well as a tendency towards entropy, layering and the disintegration of form through destructive processes such as deformation, perforation, incision, scratching, the accumulation of structures and masses, fragmentation, stripping and burning. In this paper, theoretical models of interpretation for the art of radical Informel are pointed out through the concepts of the aesthetics of ugliness, i.e. brutal aesthetics, such as (1) deformation, (2) disfiguration, (...) (3) formlessness and (4) entropy – using the example of the informal works of Croatian authors Ivo Gattin, Eugen Feller and Marijan Jevšovar, which result from their attitude towards art and painting. The artists have deliberately created paintings that are not “beautiful” by opposing the classical values of art and beauty through oppositional and negative approaches, nihilism, destruction, deformation and the abolition of the surface of the painting as forms of anti-aesthetics. (shrink)

This article attempts an organological and pharmacological re-interpretation of the later Heidegger’s understanding of modern technology as a provocative mode of revealing of beings, in particular of its central notions of Gestell [enframing] Gefahr [danger], Kehre [turning] and Ereignis [event]. Although these notions in principle allow us to think what is at stake currently in the Anthropocene as the age of total automation, generalized toxicity of the technical milieu and post-truth calling for a radical bifurcation, they need to be reframed (...) and re-imagined in terms of the process of exosomatization issuing from humanity’s original and necessary default of origin and situated within the perspective of entropy and negentropy, both unthought by Heidegger. Only thus will it become possible to really think and take care of what Heidegger called the danger of technology and its turning into the event as the destiny of enframing. This also requires a rethinking of Aristotle’s theory of four causes as it is invoked by Heidegger in his analysis of technology, in particular the efficient and final causes, in terms of what Deleuze called quasi-causality, here understood as the need and the obligation for mortals to make their fault come true, i.e., to make it truly happen or make it advene in truth, out of the experience of the danger as the ordeal of the necessary default. Thus becoming the anti-anthropic cause of anthropic toxicity, humans would restore final causality as quasi-causality and inaugurate, as neganthropos, the bifurcation into the Neganthropocene. (shrink)

The human quest for meaning is an attempt to bring experience into conjunction with illuminating concepts. The second law of thermodynamics is of wide human concern, because it touches experience which is existentially charged and therefore which humans must interpret in broad metaphysical terms. Five types of experience have been incorporated into the second law: running down, degeneracy, mixed‐up‐ness, irreversibility of time, and emergence of new possibilities. The dominant Western tradition (Plato) places these experiences within a metaphysical scheme that evaluates (...) them negatively, whereas a minority tradition (Berdyaev) evaluates them positively. The former makes entropy anti‐God; the latter places entropy within God. (shrink)

We continue to explore the consequences of Thermal Relativity Theory to the physics of black holes. The thermal analog of Lorentz transformations in the tangent space of the thermodynamic manifold are studied in connection to the Hawking evaporation of Schwarzschild black holes and one finds that there is no bound to the thermal analog of proper accelerations despite the maximal bound on the thermal analog of velocity given by the Planck temperature. The proper entropic infinitesimal interval corresponding to the Kerr–Newman (...) black hole involves a \ non-Hessian metric with diagonal and off-diagonal terms of the form \^2 = g_{ ab } d Z^a dZ^b\), where \ are the mass, charge and angular momentum, respectively. Since the computation of the scalar curvature associated to this metric is very elaborate, to simplify matters, we focused on the singularities of the metric and found that they correspond to the extremal Kerr–Newman black hole case \ with vanishing temperature. Black holes in asymptotically Anti de Sitter spacetimes are more subtle to study since the mass turns out to be related to the enthalpy rather that the internal energy. We finalize with some remarks about the thermal-relativistic analog of proper force, the need to extend our analysis of Gibbs-Boltzmann entropy to the case of Reny and Tsallis entropies, and to complexify spacetime. (shrink)

If we may rely for our evidence on simple observation, it would appear that the tendency of random or unguided activity in external nature is opposed to the development of complex organization and favorable to structural simplicity—in the sense of uniformity in the distribution of elements. This anti-organizing trend of purely physical processes is illustrated in ordinary large-scale mixing and stirring operations, as well as in the automatic increase of entropy with time in systems subject to the laws (...) of thermodynamics. It is common experience that complex systems which are the seat of physical activity tend to become simpler when left to themselves, i.e., they lose organization. Recently Eddington has given the whole matter an admirably clear expression: “Entropy may most conveniently be described as the measure of disorganization of a system.... We can see chance creeping in where formerly it was excluded.” Unless counteracted by directive action the casual or random element in nature tends to increase. If things are left to chance, not only does organization of any high degree of complexity fail to develop, but what organization there is tends to lapse or disappear. Hence in those cases, such as living organisms, where the existence and activity of the system depend on a special and complex organization, it appears necessary to assume the continued operation of a stable directive influence or factor which pervades the whole system and excludes or compensates casual factors as far as possible. The presence of this factor is what makes possible the development and maintenance of the organization required for vital activity. (shrink)

Creation and evolution were historic allies against eternalism. However, Darwinism seemed to undercut cosmological theism and human dignity, and modern reconcilers of evolution and theology have not convinced opponents that they can preserve these concerns. Creationists find divine handiwork in natural order and freedom in human uniqueness. For them, even entropy and continuity of kinds are emblematic of the unity of nature and the needfulness of salvation. Anti‐evolutionists’ impatience and frustration are not well answered by dogmatic or mythicized (...) science. Neither is creation well served by reduction to merely empiric facts. Because creationism and evolutionism rest on the unabstractable categories of contingency and necessity, neither will disappear. (shrink)

The most powerful assumption in French semiotic thought since Saussure has been the notion that a sign consists not of a name and the object it refers to, but of a sound-image and a concept, a signifier and a signified. Saussure, as amplified by Roland Barthes and others, has taught us to recognize an unbridgeable gap between words and things, signs and referents. The whole notion of "sign and referent" has been rejected by the French structuralists and their followers as (...) too materialistic and simple minded. Signs do not refer to things, they signify concepts, and concepts are aspects of thought, not aspects of reality. This elegant and persuasive formulation has certainly provided a useful critique of naive realism, vulgar materialism, and various other-isms which can be qualified with crippling adjectives. But it hasn't exactly caused the world to turn into a concept. Even semioticians eat and perform their other bodily functions just as if the world existed solidly around them. The fact that the word "Boulangerie" has no referent does not prevent them from receiving their daily bread under that sign. As Borges put it: "The world, alas, is real; I, alas, am Borges." Obviously, the whole question of the relationship between words and things cannot be debated without any assistance from nonverbal experience seems to me highly unlikely. In my view, if language really were a closed system, it would be subject, like any other closed system, to increase in entropy. In fact, it is new input into language from nonverbal experience that keeps language from decaying. Robert Scholes, professor of English and director of the program in semiotic studies at Brown University, is co-author of The Nature of Narrative and author of Structuralism in Literature. A Guggenheim fellow for 1977-78, he is currently working on "A Semiotics of Fiction." He has also contributed "Language, Narrative, and Anti-Narrative" to Critical Inquiry. (shrink)

The major global challenges of our time, like climate and environmental crises, rising inequality, the emergence of disruptive technologies, etc., demand interdisciplinary research for effective solutions. A clear understanding of value is essential for guiding socio-cultural and economic transitions to address these issues. Despite numerous attempts to define value, existing approaches remain inconsistent across disciplines and lack a comprehensive framework. This paper introduces a novel perspective on value through the lens of granular interaction thinking theory, proposing an informational entropy-based (...) notion of value. Grounded on quantum mechanics, Shannon’s information theory, and the mindsponge theory, this framework integrates both subjective and objective considerations and is highly compatible with interdisciplinary research. The informational entropy-based notion of value effectively bridges diverse concepts of value, including use and exchange value in economics, personal values in psychology, and cultural, moral, ethical, and aesthetic values in society. By offering a unifying perspective, granular interaction thinking theory provides a valuable framework for translating insights from quantum mechanics into socio-cultural, economic, and psychological contexts, enriching theoretical discourse and enhancing analytical effectiveness. (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)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the (...) most important notions of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f = {f(x,v)} and the total energy E. We find that S(ft,E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of S(Mt) = S(MXt) should hold generally for ‘‘typical’’ (the overwhelming majority of) initial microstates (phase (...) points) X0 belonging to the initial macrostate M0, satisfying MX0 = M0. This is a consequence of Liouville's theorem when Mt evolves according to an autonomous deterministic law. (shrink)

A typical claim in anti-representationalist approaches to cognition such as ecological psychology or radical embodied cognitive science is that ecological information is sufficient for guiding behavior. According to this view, affordances are immediately perceptually available to the agent (in the so-called “ambient energy array”), so sensory data does not require much further inner processing. As a consequence, mental representations are explanatorily idle: perception is immediate and direct. Here we offer one way to formalize this direct-perception claim and identify some (...) important limits to it. We argue that the claim should be read as saying that successful behavior just implies picking out affordance-related information from the ambient energy array. By relying on the Partial Information Decomposition framework, and more concretely on its development of the notion of synergy, we show that in multimodal perception, where various energy arrays carry affordance-related information, the “just pick out affordance-related information” approach is very inefficient, as it is bound to miss all synergistic components. Efficient multimodal information combination requires transmitting sensory-specific (and not affordance-specific) information to wherever it is that the various information streams are combined. The upshot is that some amount of computation is necessary for efficient affordance reconstruction. (shrink)

Michel Serres’s philosophy of entropy takes what he famously calls the ‘Northwest Passage’ between the sciences and the humanities. By contextualizing his approach to entropy and affirming the role of a philosophy of difference, this paper explores Serres’s approach by means of ‘entropic differences’. It claims that entropy – or rather, entropies – provide Serres with a paradigmatic case for critical translations between different domains of knowledge. From his early Hermès series, through to The Birth of Physics (...) and later writings on social and ethical themes, he keeps thermodynamical and informational – or ‘hard’ and ‘soft’ – understandings of entropy apart, while simultaneously exploring their relation. By focusing on the systematic significance of Serres’s ‘entropic difference’, this paper shows how it unfolds not necessarily as an ontological difference but as an operative function between the history and philosophy of science, epistemology, and a theory of negentropic (inter)subjectivity. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...) paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

This book is about an important issue which has arisen within two of the branches of physical science - namely thermodynamics and statistical mechanics - where the notion of entropy plays an essential role. A number of scientists and information theorists have maintained that entropy is a subjective concept and is a measure of human ignorance. Such a view, if it is valid, would create some profound philosophical problems and would tend to undermine the objectivity of the scientific (...) enterprise. Whilst the present volume is not a treatise on thermodynamics or statistical mechanics, all relevant steps in the building up of these disciplines are carefully scrutinised and it is concluded that the charge of subjectivity cannot be upheld. The widely adopted view that entropy is a measure of disorder, or of lack of information, is shown to be ambiguous, although it may be of use in certain contexts. (shrink)

For the first time Entropy has been completely revised and updated to include a new subtitle which reflects the expanded focus on the greenhouse effect--the largest crisis ever to face mankind.

A recent study suggests that value and quantum states seem to be governed by the same underlying mechanisms. In our recent book titled "Better economics for the Earth: A lesson from quantum and information theories," specifically Chapter 5, we have proposed an informational entropy-based notion of value, grounded in Granular Interaction Thinking Theory (GITT), which integrates granular worldview and primary features of quantum mechanics, Shannon’s information theory, and the mindsponge theory. Specifically, the notion suggests that values are created through (...) the interactions of information. But how do information and its interactions lead to values? This research note aims to contribute to the answer to this question. (shrink)

Open peer commentary on the article “The Circular Conditions of Second-order Science Sporadically Illustrated with Agent-based Experiments at the Roots of Observation” by Manfred Füllsack. Upshot: Observers construct an internal, local state of order for the perspective of their observations, but in doing so they increase the overall entropy of the system they belong to, e.g., society, by adding more options for potential courses of action. Thus, the Second Law of Thermodynamics is not just satisfied in the circular condition (...) of second-order observations, but the increase in entropy is actually exploited as a resource by a system such as society, where it serves as a prerequisite for double contingency. (shrink)

"By combining recent advances in the physical sciences with some of the novel ideas, techniques, and data of modern biology, this book attempts to achieve a new and different kind of evolutionary synthesis. I found it to be challenging, fascinating, infuriating, and provocative, but certainly not dull."--James H, Brown, University of New Mexico "This book is unquestionably mandatory reading not only for every living biologist but for generations of biologists to come."--Jack P. Hailman, Animal Behaviour , review of the first (...) edition "An important contribution to modern evolutionary thinking. It fortifies the place of Evolutionary Theory among the other well-established natural laws."--R.Gessink, TAXON. (shrink)

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, (...) extend quite generally to what we call here “causal horizons.” The root of this generalization is the local notion of horizon entropy density. (shrink)

This essay is an attempt to reconcile the disturbing contradiction between the striving for order in nature and in man and the principle of entropy implicit in the second law of thermodynamics - between the tendency toward greater organization and the general trend of the material universe toward death and disorder.

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow due to an expansion of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon (...) class='Hi'>entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the “force” accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum. (shrink)

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.

The paper tries to demonstrate that the process of the increase of entropy does not explain the asymmetry of time itself because it is unable to account for its fundamental asymmetries, that is, the asymmetry of traces (we have traces of the past and no traces of the future), the asymmetry of causation (we have an impact on future events with no possibility of having an impact on the past), and the asymmetry between the fixed past and the open (...) future, To this end, the approaches of Boltzmann, Reichenbach (and his followers), and Albert are analysed. It is argued that we should look for alternative approaches instead of this, namely we should consider a temporally asymmetrical physical theory or seek a source of the asymmetry of time in metaphysics. This second approach may even turn out to be complementary if only we accept that metaphysics can complement scientific research programmes. (shrink)

This essay is an attempt to reconcile the disturbing contradiction between the striving for order in nature and in man and the principle of entropy implicit in the second law of thermodynamics - between the tendency toward greater organization and the general trend of the material universe toward death and disorder.

A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the axioms. First the Boltzmann–Planck formula is derived. Building on this formula, using the Law of Large Numbers—a basic theorem of probability theory—the von Neumann formula is deduced. Axioms used in older theories on the foundations are now derived facts.

We review some notions for general quantum entropies. The entropy of the compound systems is discussed and a numerical computation of the quantum dynamical systems is carried for the noisy optical channel.

This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an "a priori" probability that is uniform, and where all MAXENT constraints are limited to 0-1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 established a sensitivity (...) of MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacian principle of Insufficient Reason also plague MAXENT theory. Result 3 builds upon the findings of Friedman and Shimony (1971; 1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes's (1978) prescription for his (1963) Brandeis Dice problem. Lastly, Result 4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events. (shrink)

Entropy and information are both emerging as currencies of interdisciplinary dialogue, most recently in evolutionary theory. If this dialogue is to be fruitful, there must be general agreement about the meaning of these terms. That this is not presently the case owes principally to the supposition of many information theorists that information theory has succeeded in generalizing the entropy concept. The present paper will consider the merits of the generalization thesis, and make some suggestions for restricting both (...) class='Hi'>entropy and information to specific arenas of discourse. (shrink)

The notion of conditional entropy is extended to noncomposite systems. The \-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the noncomposite systems. New entropic inequalities for quantum tomograms of qudit states including the single qudit states are obtained. The Araki–Lieb inequality is found for systems without subsystems.

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity in entropy calculations must be distinguished from the entropy of gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter (...) itself increases in entropy, and that (iii) the Second Law of thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse. (shrink)

The present paper is a survey of the economics of survival, a branch of ecological economics that stresses the preservation of the opportunities of future generations over an extended time horizon. It outlines the main analytical foundation of the branch – in which the concept of entropy is a major building block –, and its analysis of the interaction between the economic system and the environment. Regarding its outlook of the future, we see that the founders of the branch (...) were mainly concerned with the consequences of a serious depletion of natural resources – particularly the energetic capital of the earth. More recently, however, emphasis is being placed on problems that stem from the fragility of the global ecosystem in face of the disturbances caused by the entropic acceleration imposed by mankind. It is feared that the ongoing expansion of the scale of the economy may bring about irreversible damages to vital environmental functions, such as protection against undesirable consequences of solar radiation, maintenance of temperature within a range that will support life, and preservation of ecosystem resiliency. (shrink)

It is a fundamental cornerstone of thermodynamics that entropy (SU,V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{U,V}$$\end{document}) increases in spontaneous processes in isolated systems (often called closed or thermally closed systems when the transfer of energy as work is considered to be negligible) and achieves a maximum when the system reaches equilibrium. But with a different sign convention entropy could just as well be said to decrease to a minimum in spontaneous constant U, V processes. It (...) would then change in the same direction as the thermodynamic potentials in spontaneous processes. This article discusses but does not advocate such a change. (shrink)

Both a method of therapy and an exploration of psychic reality, free association is a fundamental element of psychoanalytical practices that refers to the way a patient is asked to describe what comes spontaneously to mind in the therapeutic setting. This paper examines the role of free association from the point of view of psychoanalysis and neuroscience in order to improve our understanding of therapeutic effects induced by psychoanalytic therapies and psychoanalysis. In this regard, we first propose a global overview (...) of the historical origins of the concept of free association in psychoanalysis and examine how Freud established its principles. Then, from Freud’s distinction between primary and secondary processes, we proceed to compare the psychoanalytic model with research originating from cognitive psychology and neuroscience. The notions of entropy and free energy appear particularly relevant at the intersection of these different domains. Finally, we propose the notion of symbolizing transmodality to describe certain specificities of symbolization processes within free association and we summarize the main functions of free association in psychoanalytic practices. (shrink)

I assess the thesis that counterfactual asymmetries are explained by an asymmetry of the global entropy at the temporal boundaries of the universe, by developing a method of evaluating counterfactuals that includes, as a background assumption, the low entropy of the early universe. The resulting theory attempts to vindicate the common practice of holding the past mostly fixed under counterfactual supposition while at the same time allowing the counterfactual's antecedent to obtain by a natural physical development. Although the (...) theory has some success in evaluating a wide variety of ordinary counterfactuals, it fails as an explanation of counterfactual asymmetry. (shrink)