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The theory of irreversible processes: Foundations of a non-equilibrium statistical ensemble formalism

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La Rivista del Nuovo Cimento Aims and scope

Abstract

A general overview on the construction of a non-equilibrium statistical mechanics ensemble formalism is presented. Such construction has been approached along the recently past twentieth century by a pleiad of distinguished scientists, their work being subsumed in a large systematization in the form of a physically sound, general and useful, theoretical framework. It includes their contributions and also incorporates some extensions and generalizations. The present contribution has been organized in sixteen items and five appendices where the main questions associated to such construction are considered and discussed. Among them are the relevant ones of choice of the basic variables, the questions of historicity and irreversibility and the approach to equilibrium. The derivation of a non-equilibrium grand-canonical statistical operator is presented. In terms of it a statistical irreversible thermodynamics can be built, which provides microscopic (mechano-statistical) foundations to phenomenological extended irreversible thermodynamics. It also provides a statistical non-linear higher-order hydrodynamics, including fluctuations, thus providing a unification of the kinetics and hydrodynamic approaches. Moreover, a brief description of an all-important accompanying non-linear quantum kinetic theory of relaxation processes is presented, as well as a response function theory and a fluctuation-dissipation theorem for far-fromequilibrium systems. The aspect of validation of the theory (comparison of theory and experiment) is reviewed in compact form. Furthermore, the derivation of the formalism is briefly discussed within the scope of a variational principle in an approach associated to information theory. Considerations on the question of the use of the formalism for dealing with systems with complex structure, small systems, and other particular situations, are presented.

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  1. Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Unicamp. 13083-970, Campinas, SP, Brazil

    R. Luzzi, Á. R. Vasconcellos & J. G. Ramos

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Chance is a cause, but it is inscrutable to the human mind.

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Luzzi, R., Vasconcellos, Á.R. & Ramos, J.G. The theory of irreversible processes: Foundations of a non-equilibrium statistical ensemble formalism. Riv. Nuovo Cim. 29, 1–82 (2006). https://doi.org/10.1393/ncr/i2006-10009-1

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