Nonequilibrium thermodynamics foundations

H. J. Kme2er, Nonequilibrium Thermodynamics and its Statistical Foundations, Clarendon Press, Oxford, 1981. 

MSN.77. 1. Prigogine, Microscopic aspects of entropy and the statistical foundations of nonequilibrium thermodynamics. Proceedings, International Symposium on Foundations of Continuum Thermodynamics, Bussaco, Delgado Domingo, M. N. R. Nina and J. H. Whitelaw, eds., Lisboa, 1974,... 

H. J. Kreuzer (1981) Nonequilibrium Thermodynamics and Its Statistical Foundations, Oxford University Press, London. 

In Chap. 3 (Sect. 3.6), we discussed limitations of the FREZCHEM model that were broadly grouped under Pitzer-equation parameterization and mathematical modeling. There exists another limitation related to equilibrium principles. The foundations of the FREZCHEM model rest on chemical thermodynamic equilibrium principles (Chap. 2). Thermodynamic equilibrium refers to a state of absolute rest from which a system has no tendency to depart. These stable states are what the FREZCHEM model predicts. But in the real world, unstable (also known as disequilibrium or metastable) states may persist indefinitely. Life depends on disequilibrium processes (Gaidos et al. 1999 Schulze-Makuch and Irwin 2004). As we point out in Chap. 6, if the Universe were ever to reach a state of chemical thermodynamic equilibrium, entropic death would terminate life. These nonequilibrium states are related to reaction kinetics that may be fast or slow or driven by either or both abiotic and biotic factors. Below are four examples of nonequilibrium thermodynamics and how we can cope, in some cases, with these unstable chemistries using existing equilibrium models. 

In the 1940s and 1950s, based on foundations laid down by Onsager, Ilya Prigogine (a Nobel Prize winner in 1977) developed an extension of nonequilibrium thermodynamics for systems far from equilibrium. Born in Moscow just before the Bolshevik Revolution, his family eventually left Russia to settle in Belgium. Though he originally... 

In general, the diagonal elements of a positive definite matrix must be positive. In addition, a necessary and sufficient condition for a matrix Lg to be positive definite is that its determinant and all the determinants of lower dimension obtained by deleting one or more rows and columns must be positive. Thus, according to the Second Law, the proper coefficients L k should be positive the cross coefficients, (i 7 k), can have either sign. Furthermore, as we shall see in the next section, the elements Ljk also obey the Onsager reciprocal relations Ljk = Lkj. The positivity of entropy production and the Onsager relations form the foundation for linear nonequilibrium thermodynamics. 

Strictly speaking, the chemical potential is only defined as a time-independent quantity for a system at equilibrium. Chemical kinetics belongs to the discipline of irreversible, nonequilibrium thermodynamics. Whereas thermodynamics of reversible processes has a solid foundation, this is not the case for the thermodynamics of irreversible prcx esses. At present, the latter is one of the frontier areas of chemical research. We will highlight these developments where relevant to chemical kinetics and catalysis. 

The nonequilibrium thermodynamics description of multiphase dispersions (with PAni or other substances as the disperse phase) and the resulting explanation of the formation of dissipative structures is, on the basis of present knowledge, an adequate theoretical foundation for describing the phenomena observed. 

The foundation of irreversible thermodynamics is the concept of entropy production. The consequences of entropy production in a dynamic system lead to a natural and general coupling of the driving forces and corresponding fluxes that are present in a nonequilibrium system. 

Besides immense applications, the foundations of phenomenological thermodynamics are attempted to be reformulated in nearly every textbook or monography on the subject, cf., e.g., [1-16], see also thorough discussions in [17-23]. The main reason for this situation consists in the fact that thermodynamics gives in principle only an incomplete description because the macroscopic objects it deals with are too intricate and composed of an immense number of particles the detailed behavior of which is mostly not necessary to know (disregarding the practical impossibility of such description). Moreover in nonequilibrium situations time rates and gradients of properties play an important role and thus the memory and neighborhood influences on a state in a considered time and place become more important. 

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