Quantum theory of irreversibility

A. Pérez-Madrid

Physica A: Statistical Mechanics and its Applications, 2007, vol. 378, issue 2, 299-306

Abstract: A generalization of the Gibbs–von Neumann entropy is proposed based on the quantum BBGKY (Bogolyubov–Born–Green–Kirkwood–Yvon) hierarchy as the non-equilibrium entropy for an N-body system. By using a generalization of the Liouville–von Neumann equation describing the evolution of a density superoperator, the entropy production for an isolated system is calculated, being non-zero in general. The existence of a non-zero entropy production allows us, following the procedure of non-equilibrium thermodynamics to introduce a master matrix for which a microscopic expression is obtained. After this, as a test of our theory the quantum Boltzmann equation is derived in terms of a transition superoperator related to this master matrix.

Keywords: Quantum statistical mechanics; Non-equilibrium and irreversible thermodynamics; Kinetic and transport theory of gases (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:378:y:2007:i:2:p:299-306

DOI: 10.1016/j.physa.2006.12.025

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