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.

Thermodynamics is the science that describes much of the time asymmetric behavior found in the world. This entry's first task, consequently, is to show how thermodynamics treats temporally ‘directed’ behavior. It then concentrates on the following two questions. (1) What is the origin of the thermodynamic asymmetry in time? In a world possibly governed by time symmetric laws, how should we understand the time asymmetric laws of thermodynamics? (2) Does the thermodynamic time asymmetry explain the other temporal (...) asymmetries? Does it account, for instance, for the fact that we know more about the past than the future? The discussion thus divides between thermodynamics being an explanandum or explanans. In the former case the answer will be found in philosophy of physics; in the latter case it will be found in metaphysics, epistemology, and other fields, though in each case there will be blurring between the disciplines. (shrink)

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

This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still made in subtle ways, the article explores its occurrence in three examples: the Second Law, the concept of equilibrium and the definition of phase transitions.

A distinguished American physicist and teacher delivers a landmark study thatdevelops three essential scientific themes on each subject.

According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well‐known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article takes singularities seriously and analyzes their role (...) by using the well‐known distinction between data and phenomena , in an attempt to better understand the origin of the puzzle. *Received April 2009; revised July 2009. †To contact the author, please write to: University of Cambridge, Department of History and Philosophy of Science, Free School Lane, Cambridge CB2 3RH, United Kingdom; e‐mail: [email protected]. (shrink)

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

Pictet’s experiment was front and center in the 18th/19th century debate concerning whether heat is a wave, or a particle. Pictet’s experiment is best understood by realizing that thermal radiation energy plays a significant role in heat transfer. It is argued that this readily ignored experiment should have long ago alerted us to issues concerning our understanding of thermodynamics. This questions the rationale behind modern statistical thermodynamics, which describes all of a gaseous system’s energy purely in terms of (...) the kinematics of that system’s gas. Not only is the philosophy of statistical mechanics now questioned but so too are those associated with entropy and its mathematical accomplice the second law. After raising questions, a simpler explanation as to what is witnessed will be discussed. An explanation that relegates statistical mechanics to a valid approximation for sufficiently dilute closed systems of gas, such as those often used in experiments. An explanation that remains void of the mathematical simplifications that statistical mechanics provides. Ultimately, the accepted epistemology of our sciences will be verbally challenged. (shrink)

For more than a century, physics has known of a puzzling conflict between the T- asymmetry of thermodynamic phenomena and the T-symmetry of the underlying microphysics on which these phenomena depend. This paper provides a guide to the current status of this puzzle, distinguishing the central issue from various issues with which it may be confused. It is shown that there are two competing conceptions of what is needed to resolve the puzzle of the thermodynamic asymmetry, which differ with respect (...) to the number of distinct T-asymmetries they take to be manifest in the physical world. On the preferable one-asymmetry conception, the remaining puzzle concerns the ordered distribution of matter in the early universe. The puzzle of the thermodynamic arrow thus becomes a puzzle for cosmology. (shrink)

I explore the reduction of thermodynamics to statistical mechanics by treating the former as a control theory: a theory of which transitions between states can be induced on a system by means of operations from a fixed list. I recover the results of standard thermodynamics in this framework on the assumption that the available operations do not include measurements which affect subsequent choices of operations. I then relax this assumption and use the framework to consider the vexed questions (...) of Maxwell's demon and Landauer's principle. Throughout I assume rather than prove the basic irreversibility features of statistical mechanics, taking care to distinguish them from the conceptually distinct assumptions of thermodynamics proper. (shrink)

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermody- namics of an empty box (...) allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory. (shrink)

This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down after sufficient time has gone by. Time dependent phenomena are beyond the scope of this paper. While thermodynamics is firmly rooted in statistical physics, equilibrium configurations, stability criteria and the destabilizing effect of fluctuations are all expressed in terms of thermodynamic functions. The work is not a review (...) paper but a pedagogical introduction which may interest theoreticians in astronomy and astrophysicists. It contains sufficient mathematical details for the reader to redo all calculations. References are only to seminal works or readable reviews. Delicate mathematical problems are mentioned but are not discussed in detail. (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)

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)

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)

One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way that they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is (...) a probabilistic one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his concept of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concepts that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover. (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)

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)

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

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)

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)

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.

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)

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)

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

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)

Summary Between 1911 and 1914, Owen Richardson formulated a theory of photoelectricity based on thermodynamics and statistical reasoning. Although this theory succeeded in accounting for most of the relevant phenomena and despite the lack of competing causal or descriptive accounts of the phenomena, it failed to attract other physicists. This paper seeks the reasons for the neglect of this theory in contemporary cultures of photoelectric research. Four main causes of neglect are identified: the relatively high number and the nature (...) of the theory's assumptions, the contradiction of one of these assumptions with contemporary views, the failure to suggest new predictions or to account for hitherto unexplained regularities, and the view shared by many scientists that the problem of electromagnetic radiation required a radical solution that a descriptive theory could not provide. The expectation for a radical solution defines the revolutionary character of a research field. In the case of photoelectricity, it originated in a web of evidence to which other fields contributed. The very possibility of Richardson's theory shows that, taken separately, this phenomenon could receive an account which, unlike Einstein's light quantum, did not require deep changes in the conception of nature. (shrink)

Thermodynamic macro variables, such as the temperature or volume macro variable, can take on a continuum of allowable values, called thermodynamic macro values. Although referring to the same macro phenomena, the macro variables of Boltzmannian Statistical Mechanics (BSM) differ from thermodynamic macro variables in an important respect: within the framework of BSM the evolution of macro values of systems with finite available phase space is invariably modelled as discontinuous, due to the method of partitioning phase space into macro regions with (...) sharp, fixed boundaries. Conceptually, this is at odds with the continuous evolution of macro values as described by thermodynamics, as well as with the continuous evolution of the micro state assumed in BSM. This discrepancy I call the discontinuity problem. I show how it arises from BSM’s framework and demonstrate its consequences, in particular for the foundational project of reducing thermodynamics to BSM: thermodynamic macro values are shown to not supervene on the corresponding BSM macro values. With supervenience being a conditio sine qua non for the kind of reduction envisaged by the foundational project, the latter is in jeopardy. (shrink)

It is shown that a number of questions, usually considered philosophical rather than scientific, can be reformulated to apply to a world of automata or "well-informed heat engines." In some cases they admit of physical answers, but in many cases obtaining answers entails violation of the second law of thermodynamics. This is demonstrated explicitly for the problem of determinism and free will, for the discovery of the origin or ultimate fate of the universe, or for the discovery of causes (...) or purposes in nature. (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)

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)

During the late nineteenth century, interest in thermodynamics led to several attempts to apply it to the puzzling phenomena of phosphorescence and fluorescence. These efforts reveal the pervasiveness of heat concepts for both experimental and theoretical physics of the period. The hegemony of heat concepts and theories provided a matrix for the development of quantum theory. Simultaneously, it prevented scientists from understanding cold light. Since fluorescence and phosphorescence defied basic expectations of thermodynamics and radiation theory, they contributed in (...) a minor way to the development and acceptance of quantum theory, particularly through the concept of luminescence temperature and the thermodynamic analyses of Stokes' law. Post-war theories of phosphorescence and fluorescence preserved elements of the nineteenth-century models. (shrink)

This essay focuses on the place of the second law of thermodynamics in Wilhelm Ostwald's physical chemistry. After a brief introduction to his energetic theory, which was supposed to be a generalization of thermodynamics, I contrast Ostwald's understanding of the second law, which ignored entropy and irreversibility, with Max Planck's, which emphasized both. I then consider how Ostwald sought to develop physical chemistry without any concern for irreversibility and little concern for entropy, and I argue that he was (...) mistaken. (shrink)

The basic features of thermodynamics as the “science of the possible” are outlined with a special emphasis on the role of the concept of entropy as a measure of irreversibility in natural processes and its relation to “order,” precisely defined. Natural processes may lead to an increase in complexity, and this concept has a subtle relationship to those of order, organization, and information. These concepts are analyzed with respect to their relation to biological evolution, together with other ways of (...) attempting to quantify it. Thermodynamic interpretations of evolution are described and critically compared, and the significance of dissipative structures, of “order through fluctuations,” is emphasized in relation both to the evolutionary succession of temporarily stable forms and to kinetic mechanisms producing new patterns. (shrink)

An analysis is carried out involving reversible thermodynamic operations on arbitrarily shaped small cavities in perfectly conducting material. These operations consist of quasistatic deformations and displacements of cavity walls and objects within the cavity. This analysis necessarily involves the consideration of Casimir-like forces. Typically, even for the simplest of geometrical structures, such calculations become quite complex, as they need to take into account changes in singular quantities. Much of this complexity is reduced significantly here by working directly with the change (...) in electromagnetic fields as a result of the deformation and displacement changes. A key result of this work is the derivation that for such cavity structures, classical electromagnetic zero-point radiation is the appropriate spectrum at a temperature of absolute zero to ensure that the reversible deformation operations obey both isothermal and adiabatic conditions. In addition, a generalized Wien displacement law is obtained from the demand that the change in entropy of the radiation in these arbitrarily shaped structures must be a state function of temperature and frequency. (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)

Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking their idea was that a definite temperature can be attributed to a system only if it is submerged in a heat bath, in which case energy fluctuations are unavoidable. On the other hand, a definite energy can be assigned only to systems in thermal isolation, thus excluding the simultaneous determination of its temperature. Rosenfeld (...) extended this analogy with quantum mechanics and obtained a quantitative uncertainty relation in the form ΔU Δ(1/T) ≥ k, where k is Boltzmann's constant. The two “extreme” cases of this relation would then characterize this complementarity between isolation (U definite) and contact with a heat bath (T definite). Other formulations of the thermodynamical uncertainty relations were proposed by Mandelbrot (1956, 1989), Lindhard (1986), and Lavenda (1987, 1991). This work, however, has not led to a consensus in the literature. It is shown here that the uncertainty relation for temperature and energy in the version of Mandelbrot is indeed exactly analogous to modern formulations of the quantum mechanical uncertainty relations. However, his relation holds only for the canonical distribution, describing a system in contact with a heat bath. There is, therefore, no complementarily between this situation and a thermally isolated system. (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)

Black hole thermodynamics is regarded as one of the deepest clues we have to a quantum theory of gravity. It motivates scores of proposals in the field, from the thought that the world is a hologram to calculations in string theory. The rationale for BHT playing this important role, and for much of BHT itself, originates in the analogy between black hole behavior and ordinary thermodynamic systems. Claiming the relationship is “more than a formal analogy,” black holes are said (...) to be governed by deep thermodynamic principles: what causes your tea to come to room temperature is said additionally to cause the area of black holes to increase. Playing the role of philosophical gadfly, we pour a little cold water on the claim that BHT is more than a formal analogy. First, we show that BHT is often based on a kind of caricature of thermodynamics. Second, we point out an important ambiguity in what systems the analogy is supposed to govern, local or global ones. Finally, and perhaps worst, we point out that one of the primary motivations for the theory arises from a terribly controversial understanding of entropy. BHT may be a useful guide to future physics. Only time will tell. But the analogy is not nearly as good as is commonly supposed. (shrink)