Thermodynamics classical/thermostatics

In thermodynamics (or more accurately, thermostatics) the principal contribution of information theory is to redefine the basic ideas of classical thermostatics along the lines forecast by Rothstein. The first quantitative treatment was published in 1961, followed by a textbook and later a sequence of papers (12, 13, 14, 15, 16, 17, 18, 19, 20, 21). ... 

Tribus, Myron Evans, Robert B. A Minimum Statistical Mechanics from Which Classical Thermostatics May Be Derived, in the book, "A Critical Review of Thermodynamics," Mono Book Co., Baltimore, MD, 1970. 

Non-equilibrium thermodynamics of a completely open system also enables the formation of configuration patterns in a similar way to classical thermostatics (stable crystals), but it is of a quite different dynamic nature (turbulence, vortices), showing that the dissipation can become a source of order. Microscopic characteristics of the equilibrium distribution lie in the order... 

The goal of extending classical thermostatics to irreversible problems with reference to the rates of the physical processes is as old as thermodynamics itself. This task has been attempted at different levels. Description of nonequilibrium systems at the hydrodynamic level provides essentially a macroscopic picture. Thus, these approaches are unable to predict thermophysical constants from the properties of individual particles in fact, these theories must be provided with the transport coefficients in order to be implemented. Microscopic kinetic theories beginning with the Boltzmann equation attempt to explain the observed macroscopic properties in terms of the dynamics of simplified particles (typically hard spheres). For higher densities kinetic theories acquire enormous complexity which largely restricts them to only qualitative and approximate results. For realistic cases one must turn to atomistic computer simulations. This is particularly useful for complicated molecular systems such as polymer melts where there is little hope that simple statistical mechanical theories can provide accurate, quantitative descriptions of their behavior. 

Ecosystems are open systems. Their boundaries are permeable, permitting energy and matter to cross them. Effects of environmental constraints and influences on the system play an important role in the regulation and maintenance of the system s spatio-temporal as well as trophic organization and functioning. Indeed, ecosystems operate outside the realm of classical thermodynamics. Biological, chemical, and some physical processes inside of ecosystems are nonlinear. Stationary states of ecosystems are non-equilibrium states far from thermostatic equilibrium. In the course of time, entropy does not tend to a maximum value, or entropy production to a minimum. Entropy decreases when the order of organization and structure of the ecosystem increases. Entropy production is counterbalanced by export of entropy out of the system. 

Thermodynamics and an Introduction to Thermostatics by H. B. Callen, John Wiley and Sons, New York New York, 1985. The perceptive reader will recognize on short order my own affinity for the book of Callen. His treatment of the central ideas of both thermodynamics and statistical mechanics is clean and enlightening, and I share the author s view that classical thermodynamics is primarily a theory of thermostatics. 

Prigogine attacked the daunting problem of irreversible processes and non-equihbrium thermodynamics, especially s) tems in states far from equilibrium, starting in 1945. With wry humor, he dubbed classical thermodynamics thermostatics and apphed his non-equihbrium thermodynamics to problems of biological organization and even to broader societal and philosophical questions. In 1977 Ilya Prigogine received the Nobel Prize in chemistry for his applications of thermodynamics to irreversible processes. 

Complex systems such as solutions of macromolecules, magnetic hysteresis bodies, visco-elastic fluids, polarizable media require some extra variables in the fundamental equation of Gibbs. Dissipative fluxes (heat, diffusion, viscous pressure tensor and viscous pressure) are included in the Gibbs function in new formalism. In the formalism of extended irreversible thermodynamics (EIT), the dissipative fluxes are the independent variables in addition to classical variables of thermostatics [1]. 

In a steady state the properties of a system are independent of time. If there exists a special reference frame in which all mass elements in the body are at rest and if no heat is exchanged with the surroundings the state is called a thermodynamic equilibrium state. Classical Thermo dynamics deals exclusively with such equilibrium states and it has aptly been suggested to name it thermostatics instead. Nevertheless, the name thermodynamics has persisted and we will also continue to use it. Of course, the temperature is the same everywhere in a system in thermodynamic equilibrium. 

HB Callen, Thermodynamics and an Introduction to Thermostatics, 2nd edition, Wiley, New York, 1985. This book is the classic development of the axiomatic aproach to thermodynamics, in which energy and entropy, rather than temperature, are the primary concepts. 

Therefore, in classical thermodynamics (understood in the yet substandard notation of thermostatics [272,274,275,279]) we generally accept for processes the non-equality dS > dQ/T accompanied by a statement to the effect that, although rfS is a total differential, being completely determined by the states of system, dQ is not. This has the very important consequence that in an isolated system, dQ = 0, and entropy has to increase. In isolated systems, however, processes move towards equilibrium and the equilibrium state corresponds to maximum entropy. In true non-equilibrium thermodynamics, the local entropy follows the formalism of extended thermodynamics where gradients are... 

In general the net macroscopic pressure tensor is determined by two different molecular effects One pressure tensor component associated with the pressure and a second one associated with the viscous stresses. For a fluid at rest, the system is in an equilibrium static state containing no velocity or pressure gradients so the average pressure equals the static pressure everywhere in the system. The static pressure is thus always acting normal to any control volume surface area in the fluid independent of its orientation. For a compressible fluid at rest, the static pressure may be identified with the pressure of classical thermodynamics as may be derived from the diagonal elements of the pressure tensor expression (2.189) when the equilibrium distribution function is known. On the assumption that there is local thermodynamic equilibrium even when the fluid is in motion this concept of stress is retained at the macroscopic level. For an incompressible fluid the thermodynamic, or more correctly thermostatic, pressure cannot be deflned except as the limit of pressure in a sequence of compressible fluids. In this case the pressure has to be taken as an independent dynamical variable [2] (Sects. 5.13-5.24). 

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