According to the free energy principle, life is an “inevitable and emergent property of any random dynamical system at non-equilibrium steady state that possesses a Markov blanket” :20130475, 2013). Formulating a principle for the life sciences in terms of concepts from statistical physics, such as random dynamical system, non-equilibrium steady state and ergodicity, places substantial constraints on the theoretical and empirical study of biological systems. Thus far, however, the physics foundations of the free energy principle have received hardly (...) any attention. Here, we start to fill this gap and analyse some of the challenges raised by applications of statistical physics for modelling biological targets. Based on our analysis, we conclude that model-building grounded in the free energy principle exacerbates a trade-off between generality and realism, because of a fundamental mismatch between its physics assumptions and the properties of actual biological targets. (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)

Here, we analyze how the set of nucleotides in the cell is equilibrated and how this generates simple rules that help the cell to organize itself via maintenance of a stable non‐equilibrium state. A major mechanism operating to achieve this state is thermodynamic buffering via high activities of equilibrating enzymes such as adenylate kinase. Under stable non‐equilibrium, the ratios of free and Mg‐bound adenylates, Mg2+ and membrane potentials are interdependent and can be computed. The adenylate status is balanced (...) with the levels of reduced and oxidized pyridine nucleotides through regulated uncoupling of the pyridine nucleotide pool from ATP production in mitochondria, and through oxidation of substrates non‐coupled to NAD+ reduction in peroxisomes. The set of adenylates and pyridine nucleotides constitutes a generalized cell energy status and determines rates of major metabolic fluxes. As the result, fluxes of energy and information become organized spatially and temporally, providing conditions for self‐maintenance of metabolism. (shrink)

This thesis describes a method to control rare events in non-equilibrium systems by applying physical forces to those systems but without relying on numerical simulation techniques, such as copying rare events. In order to study this method, the book draws on the mathematical structure of equilibrium statistical mechanics, which connects large deviation functions with experimentally measureable thermodynamic functions. Referring to this specific structure as the "phenomenological structure for the large deviation principle", the author subsequently extends it to time-series (...) statistics that can be used to describe non-equilibrium physics. The book features pedagogical explanations and also shows many open problems to which the proposed method can be applied only to a limited extent. Beyond highlighting these challenging problems as a point of departure, it especially offers an effective means of description for rare events, which could become the next paradigm of non-equilibrium statistical mechanics. (shrink)

Moulines in his "A Logical Reconstruction of Simple Equilibrium Thermodynamics" shows that Sneedian constraints play an essential role even in the purely theoretical development of the mathematical formalism of at least one actual scientific theory. However, Moulines' treatment is apparently inconsistent because of the way he represents constraints. A very simple non-Sneedian way of representing constraints is given which removes the difficulty.

At present classical physics contains two contradictory groups of derivations of the equilibrium spectrum of random classical electromagnetic radiation. One group of derivations finds Planck's spectrum based upon the use of classical electromagnetic zero-point radiation and fundamental ideas of thermodynamics. The other group of derivations finds the Rayleigh-Jeans spectrum from scattering equilibrium for non-linear mechanical systems in the limit of small charge coupling to radiation. Here we examine the scaling symmetries of classical thermal radiation. We find that, (...) in general, classical mechanical systems do not share the scaling symmetries of thermal radiation. In particular, this is true for the mechanical scattering systems used in the derivations of the Rayleigh-Jeans law. Indeed, relativistic hydrogenlike systems with Coulomb potentials of fixed charge are the only mechanical potential systems which do share the scaling symmetries of thermal radiation. We propose that only these last mechanical systems are allowed in a classical electromagnetic description of nature. (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.

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)

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)

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)

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of (...) typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (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)

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)

This paper presents a numerical study of the reaction A ↔ B in the presence of an intermediate and destabilizing step in its dynamics. After introducing a direct autocatalytic destabilizing process, namely quadratic autocatalysis ) and cubic autocatalysis ), a thermodynamic analysis of the evolution of the reaction in closed and open systems was performed. In addition, the Gibbs free energy, the thermodynamic affinity, and the entropy generation of the overall reaction were evaluated for each of the autocatalytic steps, in (...) order to analyze the behavior of these thermodynamic quantities when the system moved towards equilibrium or towards oscillatory non-equilibrium states. (shrink)

In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to account (...) for the non-equilibrium part of the laws of thermodynamics. Rather, we have to weaken the requirement that equilibrium be identified with a stationary probability distribution. (shrink)

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of (...) typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (shrink)

In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we have addressed the mechanical foundations of equilibrium thermodynamics on the basis of the Generalized Helmholtz Theorem. It was found that the volume entropy provides a good mechanical analogue of thermodynamic entropy because it satisfies the heat theorem and it is an adiabatic invariant. This property explains the ``equal'' sign in Clausius principle ($S_f \geq S_i$) in a purely mechanical way and suggests that the (...) volume entropy might explain the ``larger than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations were considered. Based on the principles of microscopic (quantum or classical) mechanics here we prove that, provided the initial equilibrium satisfy the natural condition of decreasing ordering of probabilities, the expectation value of the volume entropy cannot decrease for arbitrary transformations performed by some external sources of work on a insulated system. This can be regarded as a rigorous quantum mechanical proof of the Second Law. We discuss how this result relates to the Minimal Work Principle and improves over previous attempts. The natural evolution of entropy is towards larger values because the natural state of matter is at positive temperature. Actually the Law of Entropy Decrease holds in artificially prepared negative temperature systems. (shrink)

I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; the central role of Hawking (...) radiation in permitting black holes to be in thermal contact with one another; the wide range of routes by which Hawking radiation can be derived and its back-reaction on the black hole calculated; the interpretation of Hawking radiation close to the black hole as a gravitationally bound thermal atmosphere. In an appendix I discuss recent criticisms of black hole thermodynamics by Dougherty and Callender. This paper confines its attention to the thermodynamics of black holes; a sequel will consider their statistical mechanics. (shrink)

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)

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)

This chapter draws on insights from non-equilibrium thermodynamics to demonstrate the ontological inadequacy of the machine conception of the organism. The thermodynamic character of living systems underlies the importance of metabolism and calls for the adoption of a processual view, exemplified by the Heraclitean metaphor of the stream of life. This alternative conception is explored in its various historical formulations and the extent to which it captures the nature of living systems is examined. Following this, the chapter considers (...) the metaphysical implications of reconceptualizing the organism from complex machine to flowing stream. What do we learn when we reject the mechanical and embrace the processual? Three key lessons for biological ontology are identified. The first is that activity is a necessary condition for existence. The second is that persistence is grounded in the continuous self-maintenance of form. And the third is that order does not entail design. (shrink)

A major goal of science is to discover laws that underlie all regular phenomena. This goal is best satisfied by eternal principles that leave fundamental properties unchanged and unchangeable. Science has been forced to accept that some processes, especially biological processes, are inherently time oriented. It can either forgo the ideal of universal principles, and account for temporality through specific boundary conditions, or else incorporate the sources of change directly into fundamental principles that are the same for all times and (...) places, and for all temporal scales. In the past, unifying principles adequate for biology have caused trouble for physics, and vice versa. Recent work at the intersection of non-equilibrium statistical mechanics and information theory suggests that physics and biology can finally be reconciled. (shrink)

The notion of non-equilibrium, in the sense of a particle distribution other than rho equal psi squared, is imported into Nelson’s stochastic mechanics, and described in terms of effective wavefunctions obeying non-linear equations. These techniques are applied to the discussion of non-locality in non-linear Schroedinger equations.

Boltzmannian statistical mechanics (BSM) partitions a system’s space of micro-states into cells and refers to these cells as ‘macro-states’. One of these cells is singled out as the equilibrium macro-state while the others are non-equilibrium macro-states. It remains unclear, however, how these states are characterised at the macro-level as long as only real-valued macro-variables are available. We argue that physical quantities like pressure and temperature should be treated as field-variables and show how field variables fit into the framework (...) of our own version of BSM, the long-run residence time account of BSM. The introduction of field variables into the theory makes it possible to give a full macroscopic characterisation of the approach to equilibrium. (shrink)

An attempt is made to clarify a thought experiment introduced by P. T. Landsberg concerning the relativistic heat flow between bodies in relative motion. It is shown that if the problem is analyzed within the covariant thermodynamics developed by R. Balescu, supplemented by the second law of thermodynamics as proposed here, then such heat flow considerations do not fix the transformation of temperature as Landsberg contends. Instead, the transformation of temperature is left as being purely a matter of (...) definition. (shrink)

The extension of quantum mechanics to a general functional space (“rigged Hilbert space”), which incorporates time-symmetry breaking, is applied to construct extract dynamical models of entropy production and entropy flow. They are illustrated by using a simple conservative Hamiltonian system for multilevel atoms coupled to a time-dependent external force. The external force destroys the monotonicity of the ℋ-function evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around the unstable (...) particles. (shrink)

Applied Natural Science: Environmental Issues and Global Perspectives will provide the reader with a complete insight into the natural-scientific pattern of the world, covering the most important historical stages of the development of various areas of science, methods of natural-scientific research, general scientific and philosophical concepts, and the fundamental laws of nature. The book analyzes the main scientific trends and developments of modern natural science and also discusses important aspects of environmental protection. Topics include: the problem of "the two cultures": (...) the mathematization of natural sciences and the informatization of society; the non-linear nature of the processes occurring in nature and society; application of the second law of thermodynamics to describe the development of biological systems; global problems of the biosphere; theory and practice of stable organic paramagnetic materials; polymers and the natural environment. Key features include: an interdisciplinary approach in considering scientific and technical problems; a discussion of general scientific trends in modern natural science, including globalization challenges in nature and society, the organic chemistry of stable paramagnetic materials, the fundamentals of the environmental chemistry of polymeric materials, etc.; a justification of applying classical (non-equilibrium) thermodynamics to studying the behavior of open (including biological) systems. (shrink)

New numerical solutions of 3+1D covariant kinetic theory are reported for nuclear collisions in the energy domain Ecm∼200 AGeV. They were obtained using the MPC 0.1.2 parton transport code employing high parton subdivision to retain Lorentz covariance. The solutions are compared to those of relativistic hydrodynamics employing Cooper–Frye isotherm freeze-out. The transport solutions follow a different dynamical path than hydrodynamics due to large dissipative effects when pQCD scattering rates and HIJING initial conditions are assumed. The transport freeze-out four-volume is sensitive (...) to the reaction rates. The final transverse momentum distributions are found to deviate by up to an order of magnitude from those of Cooper–Frye frozen hydrodynamics. (shrink)

This paper presents a new foundation of equilibrium thermodynamics based on certain ideas of T. Ehrenfest. The main result is the proof for the existence of entropy as a consequence of the conservation of energy for conservative thermal systems.

The epistemology which sees intra-specific and intra-group heterogenization, symbiotization, interactive pattern-generating and change as basic principles produces types of theories and research strategies different from the epistemology based on the notions of intra-specific and intra-group uniformity, competition and stabilization. In the uniformistic view, individual variations have been reduced mainly either to statistical deviations from the mean or to dominance relationship. On the other hand in the heterogenistic view, mutual beneficial interactions between qualitatively heterogeneous individuals within a group is regarded as (...) indispensable for the increase of the level of behavioral and biological sophistication and evolution. This article compares five epistemologies including the two mentioned above in the context of the current epistemological transition in science, particularly due to the emergence of non-equilibrium thermodynamics in physics and differentiation-amplifying reciprocal causal models in mathematics and engineering, both of which consider the universe as pattern-generating, information-creating and evolving. (shrink)

Théophile De Donder, a Belgian mathematician born in Brussels, elaborated two important ideas that created a bridge between thermodynamics and chemical kinetics. He invented the concept of the degree of advancement of a reaction, and, in 1922, he provided a precise mathematical form to the already known chemical affinity by translating Clausius’s uncompensated heat into formal language. These concepts merge in an important inequality that was the starting point for the formalization of non-equilibrium thermodynamics. The present article (...) aims to reconstruct how De Donder elaborated his ideas and developed them by exploring his teaching activity and its connection with his scientific production. Furthermore, it emphasizes the role played by the discussions with his disciples who became his collaborators. The paper analyzes De Donder’s efforts in participating in the second Solvay Chemistry Council in 1925 to call the attention of chemists to his mathematical approach. We explain why his work did not receive much attention at the time, and how, despite this, his formalization of chemical affinity became the basis for the birth of the so-called Brussels school of thermodynamics. (shrink)

Developments in science in the last few decades have led to doubts about the validity of the mechanical paradigm that has dominated science since the Scientific Revolution. The new views, coming from recently founded disciplines like non-equilibrium thermodynamics, chaos theory and the theory of dynamical systems, are rooted in physics. Nonetheless, much of their motivation comes from fields as diverse as weather prediction, ecology, economics, the study of traffic flow, and the growth of cities. Although Quantum Mechanics also (...) led to doubts about the validity of the mechanical paradigm, the new views reveal problems within classical physics itself. The implications of these developments for our understanding of space have been largely unexamined. But the close connection between the Newtonian view of space and the mechanical paradigm means that the demise of the mechanical paradigm will require a re-evaluation of our understanding of physical space. (shrink)

The problem of causality is presented in the context of the research devoted to biogenesis. The significant works concerning the philosophy of biogenesis and scientific theories of abioge­nesis have been reviewed. Special attention is paid to: (i) the role of the non-equilibrium thermo­dynamics and quantum mechanics in the explaining of causal relations involved the origins of life, (ii) the need of constructing of a quantum logic of life. It is suggested that the causal con­nection is established by an information (...) channel between a cause and its result. (shrink)

For the Life system, behind the physics being, there is a metaphysics being that poses a non-equilibrium thermodynamics system which consist high negative entropy. Western science, western philosophy, including Western rationalism, and the nonrational, post-modernism can not completely explain this being. Theyin and yang theory can clearly illustrate it. The Yin and Yang is the knowledge of metaphysics being of life, is the metaphysics theory under the law of negative entropy.

Professor Ilya Prigogine (January 25, 1917 -- May 28, 2003), Nobel Laureate 1977 in chemistry, was one of the great visionaries of our time. Not content to rest on his laurels, he continued hard technical scientific publication, often with junior colleagues, for 25 years after the Nobel Prize was awarded to him. His fields of work included non-equilibrium thermodynamics, the emergence of dissipative structures and complex behavior, and the foundations of the arrow of time in natural science. He (...) directed two major research institutions: the Center for Studies in Statistical Mechanics and Complex Systems at the University of Texas at Austin and the International Solvay Institutes for Physics and Chemistry at Brussels. (shrink)

This paper describes a theoretical framework of ecological phase transitions for modeling tree-grass dynamics and analyzing the shifts or phase transitions from one vegetation structure to another in the southern Texas landscape. This framework implements the integration of percolation theory, fractal geometry and phase transition theory as a method for modeling the spatial patterns of tree-grass dynamics, and nonlinear Markov non-equilibrium thermodynamic stability theory as a method for characterizing temporal tree-grass dynamics and phase transition. An historical sequence of aerial (...) photographs at a Prosopis - thornscrub savanna parkland site in southern Texas was used to determine the parameters of the models. The preliminary analytical result accords well with current understanding and field survey of vegetation dynamics in the southern Texas landscape. The potential of such approaches and other relevant theories such as self-organized criticality and synergetics to vegetation dynamics is also discussed. (shrink)