Concepts of Entropy and Their Applications

European Physical Journal H, The

This paper gives a historical account of the early years (1953-1983) of extended irreversible thermodynamics (EIT). The salient features of this formalism are to upgrade the thermodynamic fluxes of mass, momentum, energy, and others, to the status of independent variables, and to explore the consistency between generalized transport equations and a generalized version of the second law of thermodynamics. This requires going beyond classical irreversible thermodynamics by redefining entropy and entropy flux. EIT provides deeper foundations, closer relations with microscopic formalisms, a wider spectrum of applications, and a more exciting conceptual appeal to non-equilibrium thermodynamics. We first recall the historical contributions by Maxwell, Cattaneo, and Grad on generalized transport equations. A thermodynamic theory wide enough to cope with such transport equations was independently proposed between 1953 and 1983 by several authors, each emphasizing different kinds of problems...

Journal of Statistical Physics, 1984

A theory of macroscopic systems which takes as independent variables the slow (conserved) ones plus the fast dissipative fluxes is carefully analyzed at three levels of description: macroscopic (thermodynamic), microscopic (projection operators) and mesoscopic (fluctuation theory). Such a description is compared with the memory function approach based only on the conserved variables. We find that the first theory is richer and wider than the second one, and some misunderstandings in this connection are clarified and discussed.

Thermodynamics is a physical branch of science that governs the thermal behavior of dynamical systems from those as simple as refrigerators to those as complex as our expanding universe. The laws of thermodynamics involving conservation of energy and nonconservation of entropy are, without a doubt, two of the most useful and general laws in all sciences. The first law of thermodynamics, according to which energy cannot be created or destroyed, merely transformed from one form to another, and the second law of thermodynamics, according to which the usable energy in an adiabatically isolated dynamical system is always diminishing in spite of the fact that energy is conserved, have had an impact far beyond science and engineering. In this paper, we trace the history of thermodynamics from its classical to its postmodern forms, and present a tutorial and didactic exposition of thermodynamics as it pertains to some of the deepest secrets of the universe.

2005

The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in equilibrium. Based on the D’Alambert equation for a subsystem the generalized Liouville equation is obtained. A necessary condition for irreversibility is determined. This condition is dependence the forces of interaction of subsystems on relative velocities. The equation of motion of subsystems of potentially interacting elements is obtained. The non-potentiality of the forces of interaction of the subsystems consisting of potentially interacting elements is proved. The mechanism of occurrence of irreversible dynamics is offered. The formula that expresses the entropy through the forces of interaction of subsystems is obtained. The theoretical link between classical mechanics and thermodynamics is analyzed.

Comptes Rendus Physique, 2007

New definitions of entropy and temperature for uniform systems that fast exchange heat with the environment are considered. Instead of the known local equilibrium hypothesis, a local uniformity hypothesis is proposed. Within the proposed formalism of extended thermodynamics of irreversible processes, dual-phase-lag transfer equations are obtained. To cite this article:

The status of heat and work in nonequilibrium thermodynamics is quite confusing and nonunique at present with conflicting interpretations even after a long history of the first law dE(t) = d e Q(t) − dW e (t) in terms of exchange heat and work, and is far from settled. Moreover, the exchange quantities lack certain symmetry (see text). By generalizing the traditional concept to also include their time-dependent irreversible components d i Q(t) and d i W (t) allows us to express the first law in a symmetric form dE(t) = dQ(t) − dW (t) in which dQ(t) and work dW (t) appear on equal footing and possess the symmetry. We prove that d i Q(t) ≡ d i W (t); as a consequence, irreversible work turns into irreversible heat. Statistical analysis in terms of microstate probabilities p i (t) uniquely identifies dW (t) as isentropic and dQ(t) as isometric (see text) change in dE(t), a result known in equilibrium. We show that such a clear separation does not occur for d e Q(t) and dW e (t). Hence, our new formulation of the first law provides tremendous advantages and results in an extremely useful formulation of non-equilibrium thermodynamics, as we have shown recently [Phys. Rev. E 81, 051130 (2010); ibid 85, 041128 and 041129 (2012)]. We prove that an adiabatic process does not alter p i. All these results remain valid no matter how far the system is out of equilibrium. When the system is in internal equilibrium, dQ(t) ≡ T (t)dS(t) in terms of the instantaneous temperature T (t) of the system, which is reminiscent of equilibrium, even though, neither d e Q(t) ≡ T (t)d e S(t) nor d i Q(t) ≡ T (t)d i S(t). Indeed, d i Q(t) and d i S(t) have very different physics. We express these quantities in terms of d e p i (t) and d i p i (t), and demonstrate that p i (t) has a form very different from that in equilibrium. The first and second laws are no longer independent so that we need only one law, which is again reminiscent of equilibrium. The traditional formulas like the Clausius inequality d e Q(t)/T 0 < 0, ∆ e W < −∆ [E(t − T 0 S(t))], etc. become equalities dQ(t)/T (t) ≡ 0, ∆W = −∆ [E(t − T (t)S(t)], etc, a quite remarkable but unexpected result in view of the fact that ∆ i S(t) > 0. We identify the uncompensated transformation N (t, τ) during a cycle. We determine the irreversible components in two simple cases to show the usefulness of our approach; here, the traditional formulation is of no use. Our extension bring about a very strong parallel between equilibrium and non-equilibrium thermodynamics, except that one has irreversible entropy generation d i S(t) > 0 in the latter.

Universidad Simón Bolívar, 2024

The main objective of this article is to present the laws of thermodynamics with a new perspective that involves a paradigm shift in the form of reasoning that has traditionally been inductive in nature, now presented with deductive characteristics. The laws are presented at the beginning in the way they are believed to be and then the different components that make them up are described.

Proceedings. Mathematical, physical, and engineering sciences / the Royal Society, 2014

The results established in contemporary statistical physics indicating that, on very small space and time scales, the entropy production rate may be negative, motivate a generalization of continuum mechanics. On account of the fluctuation theorem, it is recognized that the evolution of entropy at a material point is stochastically (not deterministically) conditioned by the past history, with an increasing trend of average entropy production. Hence, the axiom of Clausius-Duhem inequality is replaced by a submartingale model, which, by the Doob decomposition theorem, allows classification of thermomechanical processes into four types depending on whether they are conservative or not and/or conventional continuum mechanical or not. Stochastic generalizations of thermomechanics are given in the vein of either thermodynamic orthogonality or primitive thermodynamics, with explicit models formulated for Newtonian fluids with, respectively, parabolic or hyperbolic heat conduction. Several r...

We review the progress made in extended irreversible thermodynamics during the ten years that have elapsed since the publication of our first review on the same subject (Rep. Prog. Phys. 1988 51 1105–72). During this decade much effort has been devoted to achieving a better understanding of the fundamentals and a broadening of the domain of applications. The macroscopic formulation of extended irreversible thermodynamics is reviewed and compared with other non-equilibrium thermodynamic theories. The foundations of EIT are discussed on the bases of information theory, kinetic theory, stochastic phenomena and computer simulations. Several significant applications are presented, some of them of considerable practical interest (non-classical heat transport, polymer solutions, non-Fickian diffusion, microelectronic devices, dielectric relaxation), and some others of special theoretical appeal (superfluids, nuclear collisions, cosmology). We also outline some basic problems which are not yet completely solved, such as the definitions of entropy and temperature out of equilibrium, the selection of the relevant variables, and the status to be reserved to the H-theorem and its relation to the second law. In writing this review, we had four objectives in mind: to show (i) that extended irreversible thermodynamics stands at the frontiers of modern thermodynamics; (ii) that it opens the way to new and useful applications; (iii) that much progress has been achieved during the last decade, and (iv) that the subject is far from being exhausted.

Entropy, 2014

We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.