Quantum macrostatistics and irreversible thermodynamics

Abstract

We formulate a mathematical framework for the non-equilibrium statistical thermodynamics of processes of the diffusive type. Both the classical phenomenological laws and the quantum mechanical ones for the fluctuations of the relevant macro-observables are expressed in terms of tempered distributions, and the connection between these laws is formulated on the basis of very general ‘axioms’ of physical origin, which incorporate the essential ideas of the Onsager theory [1]. On this basis, we show that the fluctuation dynamics of the quantum macroobservables reduces to a classical Markov process in a certain large-scale, hydrodynamical limit, and that the phenomenological transport coefficients satisfy the Onsager reciprocity relations.

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