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

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.

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)

This paper is the first part of a three-part project ‘How the principle of energy conservation evolved between 1842 and 1870: the view of a participant’. This paper aims at showing how the new ideas of Mayer and Joule were received, what constituted the new theory in the period under study, and how it was supported experimentally. A connection was found between the new theory and thermodynamics which benefited both of them. Some considerations are offered about the desirability of (...) taking a historical approach to teaching energy and its conservation. (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)

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)

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.

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)

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)

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)

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)

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)

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)

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)

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)

Or better: time asymmetry in thermodynamics. Better still: time asymmetry in thermodynamic phenomena. “Time in thermodynamics” misleadingly suggests that thermodynamics will tell us about the fundamental nature of time. But we don’t think that thermodynamics is a fundamental theory. It is a theory of macroscopic behavior, often called a “phenomenological science.” And to the extent that physics can tell us about the fundamental features of the world, including such things as the nature of time, we generally (...) think that only fundamental physics can. On its own, a science like thermodynamics won’t be able to tell us about time per se. But the theory will have much to say about everyday processes that occur in time; and in particular, the apparent asymmetry of those processes. The pressing question of time in the context of thermodynamics is about the asymmetry of things in time, not the asymmetry of time, to paraphrase Price ( , ). I use the title anyway, to underscore what is, to my mind, the centrality of thermodynamics to any discussion of the nature of time and our experience in it. The two issues—the temporal features of processes in time, and the intrinsic structure of time itself—are related. Indeed, it is in part this relation that makes the question of time asymmetry in thermodynamics so interesting. This, plus the fact that thermodynamics describes a surprisingly wide range of our ordinary experience. We’ll return to this. First, we need to get the question of time asymmetry in thermodynamics out on the table. (shrink)

There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non-commutative special (...) relativity, and show that one arrives at a generalized quantum dynamics in which space and time are non-classical and have an operator status. In a future work, we will show how standard quantum theory on a classical space-time background is recovered from here. (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)

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)

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)

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)

Are principles of information processing necessary to demonstrate the consistency of statistical mechanics? Does the physical implementation of a computational operation have a fundamental thermodynamic cost, purely by virtue of its logical properties? These two questions lie at the centre of a large body of literature concerned with the Szilard engine (a variant of the Maxwell's demon thought experiment), Landauer's principle (supposed to embody the fundamental principle of the thermodynamics of computation) and possible connections between the two. A variety (...) of attempts to answer these questions have illustrated many open questions in the foundations of statistical mechanics. (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)

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)

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)

The thermodynamics of life Content Type Journal Article Category Book Review Pages 1-3 DOI 10.1007/s11016-012-9651-8 Authors J. Scott Turner, SUNY, College of Environmental Science and Forestry, Syracuse, NY 13210, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

Equilibrium states are used as limit states to define thermodynamically reversible processes. When these processes are implemented in statistical physics, these limit states become unstable and can change with time, due to thermal fluctuations. For macroscopic systems, the changes are insignificant on ordinary time scales and what little there is can be suppressed by macroscopically negligible, entropy-creating dissipation. For systems of molecular sizes, the changes are large on short time scales and can only sometimes be suppressed with significant entropy-creating dissipation. (...) As a result, at molecular scales, thermodynamically reversible processes are impossible in principle, even as approximations, when we account for all sources of dissipation. (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)

David Lewis ([1986b]) gives an attractive and familiar account of counterfactual dependence in the standard context. This account has recently been subject to a counterexample from Adam Elga ([2000]). In this article, I formulate a Lewisian response to Elga’s counterexample. The strategy is to add an extra criterion to Lewis’s similarity metric, which determines the comparative similarity of worlds. This extra criterion instructs us to take special science laws into consideration as well as fundamental laws. I argue that the Second (...) Law of Thermodynamics should be seen as a special science law, and give a brief account of what Lewisian special science laws should look like. If successful, this proposal blocks Elga’s counterexample. (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)

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

Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic (...) second law of causal horizon thermodynamics. (shrink)

Standard descriptions of thermodynamically reversible processes attribute contradictory properties to them: they are in equilibrium yet still change their state. Or they are comprised of non-equilibrium states that are so close to equilibrium that the difference does not matter. One cannot have states that both change and no not change at the same time. In place of this internally contradictory characterization, the term “thermodynamically reversible process” is here construed as a label for a set of real processes of change involving (...) only non-equilibrium states. The properties usually attributed to a thermodynamically reversible process are recovered as the limiting properties of this set. No single process, that is, no system undergoing change, equilibrium or otherwise, carries those limiting properties. The paper concludes with an historical survey of characterizations of thermodynamically reversible processes and a critical analysis of their shortcomings. (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)

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)

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)