The evolution equations for grain growth and coarsening have been derived in the open literature mainly based on phenomenological considerations. Applying a thermodynamic extremal principle, the evolution equations are derived in a rigorous way. All kinetic parameters are provided directly. Existing relations are proved and generalized.

Explanation of physical regularities from positions of the thermodynamic approach -- Application of the thermodynamic approach to the processes going in the human organism.

This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal (...) as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science. (shrink)

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

Recognition that biological systems are stabilized far from equilibrium by self-organizing, informed, autocatalytic cycles and structures that dissipate unusable energy and matter has led to recent attempts to reformulate evolutionary theory. We hold that such insights are consistent with the broad development of the Darwinian Tradition and with the concept of natural selection. Biological systems are selected that re not only more efficient than competitors but also enhance the integrity of the web of energetic relations in which they are embedded. (...) But the expansion of the informational phase space, upon which selection acts, is also guaranteed by the properties of open informational-energetic systems. This provides a directionality and irreversibility to evolutionary processes that are not reflected in current theory.For this thermodynamically-based program to progress, we believe that biological information should not be treated in isolation from energy flows, and that the ecological perspective must be given descriptive and explanatory primacy. Levels of the ecological hierarchy are relational parts of ecological systems in which there are stable, informed patterns of energy flow and entropic dissipation. Isomorphies between developmental patterns and ecological succession are revealing because they suggest that much of the encoded metabolic information in biological systems is internalized ecological information. The geneological hierarchy, to the extent that its information content reflects internalized ecological information, can therefore be redescribed as an ecological hierarchy. (shrink)

This article argues that most of the approaches to the foundations of statistical mechanics have severed their link with the original foundational project, the project of demonstrating how real mechanical systems can behave thermodynamically.

It is argued that certain recent advances in the construction of a theory of the collapses of Quantum Mechanical wave functions suggest the possibility of new and improved foundations for statistical mechanics, foundations in which epistemic considerations play no role.

Keywords: A theological approach to understanding time and change in a modern way must consider the relationships between thermal physics and time as elucidated during the past century and a half. The fact of temporal change, including death and decay, has been a religious problem since antiquity, so that some traditions have simply attempted to transcend the world of change. However, a major current of the Christian tradition has seen change as a fundamental aspect of God's creation, and one (...) with which God becomes identified in the Incarnation. This implies approval of history, as having an ultimate value, rather than transcendence of it.We examine thermodynamics, and especially its Second Law, in order to understand more precisely the issues of temporal change. The Second Law states a universal tendency toward increasing disorder, and several implications of this law are discussed. Of particular significance, however, is the work of Prigogine and others on nonequilibrium thermodynamics, drawing attention to such phenomena as the enhancement of chemical reaction rates and the formation of “dissipative structures” in nonequilibrium situations. Such possibilities may be of considerable importance for understanding chemical and biological evolution.These ideas can be included in an evolutionary picture in which, following Teilhard de Chardin, the Body of Christ is seen as the future of evolution‐an “ultimate dissipative structure” in which the world of time and change is united with God. Suffering, death, and decay receive their meaning from the future. Within this framework it is therefore possible to believe that the material world of history may be part of the eschatological future and that science provides hints, though not predictions, of how that may happen. (shrink)

The protein folding problem is one of the foundational problems of biochemistry and it is still considered unsolved. It basically consists of two main questions: what are the factors determining the stability of the protein’s native structure and how does the protein acquire it starting from an unfolded state. Since its first formulation, two main explanatory approaches have dominated the field of protein folding research: a thermodynamic approach focused on energetic features and a kinetic approach focused on the (...) temporal development of protein chains and structural considerations. Although these two approaches are tightly intertwined in biochemical practice and largely agree on which are the parts and activities in which the phenomenon under study should be decomposed to, there nevertheless exist important contrasts that have had repercussions on the development of the field and still engender vigorous debate. We shall analyse the historical development of the field and crucial aspects of current scientific debates. On this basis, we argue that the main sources of disagreement centre on the causal interpretation of thermodynamic and kinetic explanations, on the explanatory relevance assigned to different features of the phenomena under study and on the status of the ontological assumptions concerning the entities under study. (shrink)

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable (...) intellectual wealth—are conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set. (shrink)

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable (...) intellectual wealth—are conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set. (shrink)

Thermodynamics is an unusual theory. Prominent figures, including J.C. Maxwell and E.T. Jaynes, have suggested that thermodynamics is anthropocentric. Additionally, contemporary approaches to quantum thermodynamics label thermodynamics a ‘subjective theory’. Here, we evaluate some of the strongest arguments for anthropocentrism based on the heat/work distinction, the second law, and the nature of entropy. We show that these arguments do not commit us to an anthropocentric view but instead point towards a resource-relative understanding of thermodynamics which (...) can be shorn of the ‘subjective gloss’. (shrink)

The debate about the passage of time is usually confined to Minkowski‟s geometric interpretation of space-time. It infers the block universe from the notion of relative simultaneity. But there are alternative interpretations of space-time – so-called axiomatic approaches –, based on the existence of „optical facts‟, which have thermodynamic properties. It may therefore be interesting to approach the afore-mentioned debate from the point of view of relativistic thermodynamics, in which invariant parameters exist, which may serve to indicate the (...) passage of time. Of particular interest is the use of entropic clocks, gas clocks and statistical thermometers, which suggest that two observers in Minkowski space-time could agree on an objective passing of time. (shrink)

Dissipative structures exist at all scales, systems, and at different levels of complexity. A thermodynamic theory integrating simple and complex DS is introduced, which addresses existence of growing/decaying DS based on their entropy analysis. Two entropy-based dimensionless ratios are introduced, which explain negentropy-debt payment and existence of DS with growth or decay. It is shown that excess negentropy debt payment is needed and beneficial for growing DS; but for decaying DS, it hastens its approach to perish and is counter-productive. (...) Growing complex DS tend to pay lower negentropy debt to their surroundings, due to involvement in other activities enabled by complexity; e.g. mediation for survival that is linked to their mortality. Hence, disorder of complex DS increases, due to which, their growth can be un-sustained, leading to entry in decay-phase in spite of availability of adequate mass-energy in-flows. Proper handling or reduction of complexity enables growth in the direction of ideal growth, which is limited only by availability of adequate mass-energy in-flows. (shrink)

From 1873 to 1878, the American physicist Josiah Willard Gibbs offered to the scientific community three great articles that proved to be a milestone for the science of thermodynamics. On the other hand, between 1886 and 1896, the French physicist Pierre Maurice Marie Duhem translated thermodynamics into the language of Lagrange’s analytical mechanics. At the same time, he expanded its scope to include thermal phenomena, electromagnetic phenomena, and all kinds of irreversible processes. Duhem formulated a version of (...) class='Hi'>thermodynamics characterized by the conceptual unification of mechanics, physics, and chemistry. Overall, the work of both physicists on thermodynamics is tremendous, full of axioms, theorems, corollaries, proofs, and hundreds of equations. Therefore, it would be a utopian aim to provide a short analysis of their work. Instead, the present study will attempt to give a brief outline of the main tools and concepts used by the two physicists. I will argue that each scientist approaches thermodynamics in a new and unique way, which reveals their scientific styles as reflected in their personalities, the writing styles, their behavior toward publicity, and their inclination for publication. Finally, I will examine the influence of their theories on the development of chemical thermodynamics. (shrink)

After more than 60 years, Shannon’s research continues to raise fundamental questions, such as the one formulated by R. Luce, which is still unanswered: “Why is information theory not very applicable to psychological problems, despite apparent similarities of concepts?” On this topic, S. Pinker, one of the foremost defenders of the widespread computational theory of mind, has argued that thought is simply a type of computation, and that the gap between human cognition and computational models may be illusory. In this (...) context, in his latest book, titled Thinking Fast and Slow, D. Kahneman provides further theoretical interpretation by differentiating the two assumed systems of the cognitive functioning of the human mind. He calls them intuition (system 1) determined to be an associative (automatic, fast and perceptual) machine, and reasoning (system 2) required to be voluntary and to operate logical-deductively. In this paper, we propose a mathematical approach inspired by Ausubel’s meaningful learning theory for investigating, from the constructivist perspective, information processing in the working memory of cognizers. Specifically, a thought experiment is performed utilizing the mind of a dual-natured creature known as Maxwell’s demon: a tiny “man–machine” solely equipped with the characteristics of system 1, which prevents it from reasoning. The calculation presented here shows that the Ausubelian learning schema, when inserted into the creature’s memory, leads to a Shannon-Hartley-like model that, in turn, converges exactly to the fundamental thermodynamic principle of computation, known as the Landauer limit. This result indicates that when the system 2 is shut down, both an intelligent being, as well as a binary machine, incur the same minimum energy cost per unit of information (knowledge) processed (acquired), which mathematically shows the computational attribute of the system 1, as Kahneman theorized. This finding links information theory to human psychological features and opens the possibility to experimentally test the computational theory of mind by means of Landauer’s energy cost, which can pave a way toward the conception of a multi-bit reasoning machine. (shrink)

The recently suggested reformulation of Darwinian evolutionary theory, based on the thermodynamics of self‐organizing processes, has strong philosophical implications. My claim is that the main philosophical merit of the thermodynamic approach, made especially clear in J.S. Wicken's work, is its insistence on the law‐governed, continuous nature of evolution. I attempt to substantiate this claim following a historical analysis of beginning‐of‐the‐century ideas on evolution and matter‐life relationship, in particular, the fitness‐of‐the‐environment‐for‐life theory of the Harvard physiologist L.J. Henderson. In addition, (...) I point to an epistemological common ground underlying the studies of the “thermodynamics school” and other currently active research groups focusing on the emergence and evolution of biological organization. (shrink)

Our work is aimed at studying the optimization of a complex motor behaviour from a global perspective. First, free climbing as a sport will be briefly introduced while emphasizing in particular its psychomotor aspect called route finding. The basic question raised here is how does the optimization of a sensorimotoricity-environment system take place. The material under study is the free climber's trajectory, viewed as the signature of climbing behaviour (i.e., the spatial dimension). The concepts of learning, optimization, constraint, and degrees (...) of freedom of a system will be discussed using the synergistic approach to the study of movement (Bernstein, 1967; Kelso, 1977). Measures of a trajectory's length and convex hull can be used to define an index whose equation resembles that of an entropy. This index is a measure of the trajectory's overall complexity. Some important concepts related to the thermodynamics of curves will also be discussed. The optimization process will be studied by examining the changes in entropy over time for a set of trajectories generated during the learning of a route (ten successive repetitions of the same climb). It will be shown that the entropy of the trajectories decreases as learning progresses, that each level of expertise has its own characteristic entropy curve, and that for the subjects tested, the mean entropy of skilled climbers is lower than that of average climbers. Basing our analysis on the concepts of degrees of freedom and constraint equations, an attempt is made to relate trajectory entropy to system entropy. Based on the postulate that trajectory entropy is equal to the difference in entropy between the unconstrained and constrained system, a model of motor optimization is proposed. This model is illustrated by an entropy graph reflecting a dynamic release process. In the light of our results, two opposing views will be examined: movement construction vs. movement emergence. (shrink)

Can the second law of thermodynamics explain our mental experience of the direction of time? According to an influential approach, the past hypothesis of universal low entropy also explains how the psychological arrow comes about. We argue that although this approach has many attractive features, it cannot explain the psychological arrow after all. In particular, we show that the past hypothesis is neither necessary nor sufficient to explain the psychological arrow on the basis of current physics. We (...) propose two necessary conditions on the workings of the brain that any account of the psychological arrow of time must satisfy. And we propose a new reductive physical account of the psychological arrow of time compatible with time-symmetric physics, according to which these two conditions are also sufficient. Our proposal has some radical implications, for example, that the psychological arrow of time is fundamental, whereas the temporal direction of entropy increase in the second law of thermodynamics and the past hypothesis is derived from it, rather than the other way around. 1Introduction2A Physical Account of the Psychological Arrow of Time3Necessary Conditions for the Psychological Arrow of Time4The Psychological Arrow of Time via the Second Law of Thermodynamics and the Past Hypothesis5Why the Past Hypothesis Is Insufficient for the Psychological Arrow of Time5.1Stage 1, Version 1: From the past hypothesis to the psychological arrow via typicality5.2Stage 1, Version 2: From the past hypothesis to the psychological arrow via dynamical or causal considerations5.3Stage 2: From entropy gradient in the brain to the psychological arrow of time6Why the Past Hypothesis Is Unnecessary for the Psychological Arrow of Time7A New Reductive Account of the Psychological Arrow of Time. (shrink)

Can we explain the laws of thermodynamics, in particular the irreversible increase of entropy, from the underlying quantum mechanical dynamics? Attempts based on classical dynamics have all failed. Albert (1994a,b; 2000) proposed a way to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wavefunction of Ghirardi, Rimini and Weber (1986). In this paper we propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach (...) relies on the standard quantum mechanical models of environmental decoherence of open systems, e.g. Joos and Zeh (1985) and Zurek and Paz (1994). (shrink)

The recent surge of interest in the origin of the temporal asymmetry of thermodynamical systems (including the accessible part of the universe itself) has put forward two possible explanatory approaches to this age-old problem. Hereby we show that there is a third possible alternative, based on the generalization of the classical (“Boltzmann–Schuetz”) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann's statistical measure at its (...) face value, and accomodating it within the quantum cosmological concept of the multiverse. We argue that conventional objections raised against the Boltzmann–Schuetz view are less forceful and serious than it is usually assumed. A fortiori, they are incapable of rendering the generalized theory untenable. On the contrary, this analysis highlights some of the other advantages of the multiverse approach to the thermodynamical arrow of time. (shrink)

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

In discussing fundamentals of general-relativistic irreversible continuum thermodynamics, this theory is shown to be characterized by the feature that no thermodynamical degrees of freedom are ascribed to gravitation. However, accepting that black hole thermodynamics seems to oppose this harmlessness of gravitation one is called on to consider other approaches. Therefore, in brief some gravitational and thermodynamical alternatives are reviewed.

In discussing fundamentals of general-relativistic irreversible continuum thermodynamics, this theory is shown to be characterized by the feature that no thermodynamical degrees of freedom are ascribed to gravitation. However, accepting that black hole thermodynamics seems to oppose this harmlessness of gravitation one is called on to consider other approaches. Therefore, in brief some gravitational and thermodynamical alternatives are reviewed.

The search for the statistical mechanical underpinning of thermodynamic irreversibility has so far focussed on the spontaneous approach to equilibrium. But this is the search for the underpinning of what Brown and Uffink have dubbed the ‘minus first law’ of thermodynamics. In contrast, the second law tells us that certain interventions on equilibrium states render the initial state ‘irrecoverable’. In this article, I discuss the unusual nature of processes in thermodynamics, and the type of irreversibility that the (...) second law embodies. I then search for the microscopic underpinning or statistical mechanical ‘reductive basis’ of the second law of thermodynamics by taking a functionalist strategy. First, I outline the functional role of the thermodynamic entropy: for a thermally isolated system, the thermodynamic entropy is constant in quasi-static processes, but increasing in non-quasi-static processes. I then search for the statistical mechanical quantity that plays this role—rather than the role of the traditional ‘holy grail’ as described by Callender. I argue that in statistical mechanics, the Gibbs entropy plays this role. (shrink)

This paper examines the justifications for using infinite systems to ‘recover’ thermodynamic properties, such as phase transitions, critical phenomena, and irreversibility, from the micro-structure of matter in bulk. Section 2 is a summary of such rigorous methods as in taking the thermodynamic limit to recover PT and in using renormalization group approach to explain the universality of critical exponents. Section 3 examines various possible justifications for taking TL on physically finite systems. Section 4 discusses the legitimacy of applying TL (...) to the problem of irreversibility and assesses the repercussions for its legitimacy on its home turf. (shrink)

The second law results in the growth of the entropy – in superficial interpretation this principle presumes that the sufficient energy inevitably turns into the substandard energy. Order turns into chaos over time; however, chaos also turns into order under certain circumstances. The first research objective is to establish the possible prescientific ideas about the phenomenon – some philosophical intuitions that have preceded the scientific discovery of the second law and have conformed to it in a certain sense. It is (...) essential because there are always certain bonds and continuity in the history of philosophy and science – the correct interpretation of the phenomenon becomes difficult, if not impossible, without the establishment of such bonds.Moreover, the main task is to understand what the second law is and which significance its principal corollaries have. We need to give the second law a correct interpretation that will allow making assumptions about its connection with time in the context of the initial state problem and about the possible new ways of modern physics development – in particular, the creation of the quantum theory of gravity. Two solutions to the entropy and initial state connection problem are proposed in the context of the time arrow discussion (G. Calender’s approach to solving the problem is disputed). (shrink)

We introduce a simple model for so-called spin-echo experiments. We show that the model is a mincing system. On the basis of this model we study fine-grained entropy and coarse-grained entropy descriptions of these experiments. The coarse-grained description is shown to be unable to provide an explanation of the echo signals, as a result of the way in which it ignores dynamically generated correlations. This conclusion is extended to the general debate on the foundations of statistical mechanics. We emphasize the (...) need for an appropriate mechanism to explain the gradual suppression over time of the correlations in a thermodynamic system. We argue that such a mechanism can only be provided by the interventionist approach, in which the interaction of the system with its environment is taken into account. Irreversible behavior is then seen to arise not as a result of limited measurement accuracy , but as a result of the fact that thermodynamic systems are limited systems which interact with their environment. A detailed discussion is given of recent objections to the interventionist approach in the literature. (shrink)

We show that the so-called Multiple-Computations Theorem in cognitive science and philosophy of mind challenges Landauer’s Principle in physics. Since the orthodox wisdom in statistical physics is that Landauer’s Principle is implied by, or is the mechanical equivalent of, the Second Law of thermodynamics, our argument shows that the Multiple-Computations Theorem challenges the universal validity of the Second Law of thermodynamics itself. We construct two examples of computations carried out by one and the same dynamical process with respect (...) to which Landauer’s principle implies contradictory predictions concerning the entropy increase. Our two examples are based on a weak version of the Multiple-Computations Theorem, which is quite uncontroversial, and therefore they amount to a clear refutation of the universal validity of Landauer’s Principle. We consider some responses to this argument that do not attempt to single out one computation over the others, and we show that they do not work. We further consider ways out of the argument by externalist approaches supporting the computational theory of the mind who propose that the interaction of a computing system with the environment is enough to select a single computation over the others. We show on physical grounds that this approach fails too. We then reverse the direction of our challenge and formulate a dilemma for supporters of the computational theory of the mind: they must reject the causal closure of physic; or else they must accept on a priori grounds that Landauer’s Principle and the Second Law of thermodynamics are not universally valid. Finally, we present our version of a type–type mind-brain identity theory called Flat Physicalism, which is based on the paradigm case of statistical mechanics, and we show that it circumvents the challenge from Landauer’s Principle and the Multiple-Computations Theorem and does not fall prey to our dilemma. (shrink)

After the birth of thermodynamics’ second principle—outlined in Carnot's Réflexions sur la puissance motrice du feu —several studies provided new arguments in the field. Mainly, they concerned the thermodynamics’ first principle—including energy conceptualisation—, the analytical aspects of the heat propagation, the statistical aspects of the mechanical theory of heat. In other words, the second half of nineteenth century was marked by an intense interdisciplinary research activity between physics and chemistry: new disciplines applied to the heat developed in the (...) form of analytical, mechanical and statistical theories. Inside all these theories, entropy—the brand-new function that Clausius coined in his Mechanical theory of heat—started to play a central epistemic role. In the present paper, we analyse some steps of the historical process of conceptualisation of such function from 1850 to 1902. Particularly, we retrace the historical–foundational path that—starting from Clausius’ Second Law—lead Boltzmann and Gibbs to their distinguished formulations of statistical entropy. As usual, our research has been unrolled through the analyses of primary sources and by leaning on critical readings of the secondary literature. As for the methodological approach, text analysis of historical documents constituted our privileged modus operandi. This paper is the expression of a collaborative historical research program focused on the thermodynamic foundations of physics–chemistry relationship; early results have already been published by the same authors upon the concepts of reversibility––and––thermal equilibrium. (shrink)

Analytical models describing the motion of colloidal particles in given force fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker–Planck equations, a global description based on path integration is reviewed. A new result is presented, showing that under very broad conditions, during its evolution a dissipative system tends to minimize its energy dissipation in such a way to keep constant the Hamiltonian time rate, equal to the difference between (...) the flux-based and the force-based Rayleigh dissipation functions. In fact, the Fokker–Planck equation can be interpreted as the Hamilton–Jacobi equation resulting from such minumum principle. At steady state, the Hamiltonian time rate is maximized, leading to a minimum resistance principle. In the unsteady case, we consider the relaxation to equilibrium of harmonic oscillators and the motion of a Brownian particle in shear flow, obtaining results that coincide with the solution of the Fokker–Planck and the Langevin equations. (shrink)

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the (...) Foundations of Statistical Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way. (shrink)

In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement, that `entropy increases with time' without preferring a time direction. In this paper we try to explain this statement---which is well known since the time of the Ehrenfests---in some detail within a systematic Bayesian approach.

The connection between brain and mind is an important scientific and philosophical question that we are still far from completely understanding. A crucial point to our work is noticing that thermodynamics provides a convenient framework to model brain activity, whereas cognition can be modeled in information-theoretical terms. In fact, several models have been proposed so far from both approaches. A second critical remark is the existence of deep theoretical connections between thermodynamics and information theory. In fact, some well-known (...) authors claim that the laws of thermodynamics are nothing but principles in information theory. Unlike in physics or chemistry, a formalization of the relationship between information and energy is currently lacking in neuroscience. In this paper we propose a framework to connect physical brain and cognitive models by means of the theoretical connections between information theory and thermodynamics. Ultimately, this article aims at providing further insight on the formal relationship between cognition and neural activity. (shrink)

This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.

This paper examines the justifications for using infinite systems to 'recover' thermodynamic properties, such as phase transitions (PT), critical phenomena (CP), and irreversibility, from the micro-structure of matter in bulk. Section 2 is a summary of such rigorous methods as in taking the thermodynamic limit (TL) to recover PT and in using renormalization (semi-) group approach (RG) to explain the universality of critical exponents. Section 3 examines various possible justifications for taking TL on physically finite systems. Section 4 discusses (...) the legitimacy of applying TL to the problem of irreversibility and assesses the repercussions for its legitimacy on its home turf. (shrink)

The received view of Bergson's philosophy of life is that it advances some form of vitalism under the heading of an “élan vital.” This paper argues against the vitalistic interpretation of Bergson's élan vital as it appears in Creative Evolution in favor of an interpretation based on his overlooked reflections on entropy and energetics. Within the interpretation developed here, the élan vital is characterized not as a spiritualistic “vital force” but as a tendency of organization opposed to the tendency of (...) entropic degradation. It is then shown how Bergson's view of evolution and living organization resonates with more contemporary scientific approaches belonging to a “thermodynamic paradigm” in theoretical biology in different respects, including the critique of neo-Darwinism and the positing of a driving force behind evolution. Finally, the special interest that Bergson's philosophical biology bears today is considered in terms of the connection between the concepts of élan vital and duration. (shrink)

The new mathematical connection of De Donder’s differential entropy production with the differential changes of thermodynamic potentials (Helmholtz free energy, enthalpy, and Gibbs free energy) was obtained through the linear sequence of equations (direct, straightforward path), in which we use rigorous thermodynamic definitions of the partial molar thermodynamic properties. This new connection uses a global approach to the problem of reversibility and irreversibility, which is vital to global learners’ view and standardizes the linking procedure for thermodynamic potentials (Helmholtz free (...) energy, enthalpy, and and Gibbs free energy)—preferably to the sensing learners. It is shown that De Donder’s differential entropy production in an isolated composite system is equal to the differential change in total entropy and that De Donder’s equation agrees with Clausius’ inequality. The useful work of the irreversible process is discussed, which with the decrease of irreversibility tends towards the hypothetical maximum useful work of the reversible process. (shrink)

Scientists investigating the thermal properties of black holes rely heavily on theoretical and non-empirical tools, such as mathematical derivations, analogue experiments and thought experiments. Although the use of mathematical derivations and analogue experiments in the context of black hole physics has recently received a great deal of attention among philosophers of science, the use of thought experiments (TEs) in that context has been almost completely neglected. In this paper, we will start filling this gap by systematically analyzing the epistemic role (...) of the two TEs that gave birth to black hole thermodynamics, namely Wheeler’s demon and Geroch’s engine. We will argue that the two main epistemic functions of these TEs are to reveal and resolve inconsistencies, in line with El Skaf’s (Probing theoretical statements with thought experiments. Synthese 199:6119–6147, 2021) approach to TEs. We will, then, go beyond El Skaf’s approach by stressing an important difference between the strategies employed to assess the reliability of each epistemic function. (shrink)

Ludwig Boltzmann is one of the foremost responsible for the development of modern atomism in thermodynamics. His proposition was revolutionary not only because it brought a new vision for Thermodynamics, merging a statistical approach with Newtonian physics, but also because he produced an entirely new perspective on the way of thinking about and describing physical phenomena. Boltzmann dared to flirt with constructivism and realism simultaneously, by hypothesizing the reality of atoms and claiming an inherent probabilistic nature related (...) to many particles systems. Boltzmann faced criticism from the positivists, who rejected the hypothesis of the atom as a matter of principle, and also from physicists, who rejected the idea of a classical bounded system that does not follow deterministic mechanical laws. We consider that Boltzmann thermodynamics has emerged as a systemic theory that deals with macroscopic bodies using collective variables; it was reformulated to a kinetic theory of gases, and subsequently to statistical mechanics. From the theoretical physical point of view, Boltzmann advocates an approach to thermodynamics based on mechanics and was one of the founders of statistical mechanics, together with ideas by Maxwell, Clausius and Gibbs. Subsequently, statistical mechanics has also influenced the development of quantum mechanics and information theory. Using an evolutionary epistemological perspective as a metaphor to describe the physical entities claimed in Boltzmann propositions, we interpret his work as a selected theory that gained attributes of reality and “survived” during a scientific-contextual competition to be more adapted, in the sense that it was able to better explain physical phenomena, and also generated “descendants”. (shrink)