Irreversibility and the Arrow of Time

• URL: http://arxiv.org/abs/2202.04619v1
• Date: Wed, 9 Feb 2022 18:32:01 GMT
• Title: Irreversibility and the Arrow of Time
• Authors: J\"urg Fr\"ohlich
• Abstract summary: Irreversible behavior often manifests itself in the guise of entropy production. A derivation of the laws of thermodynamics from (quantum) statistical mechanics is presented. Results on diffusive (Brownian) motion of a quantum particle interacting with a quasi-free quantum-mechanical heat bath are reviewed.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Within the general formalism of quantum theory irreversibility and the arrow of time in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of entropy production. This motivates me to begin this paper with a brief review of quantum-mechanical entropy, a subject that Elliott Lieb has made outstanding contributions to, followed by an enumeration of examples of irreversible behavior and of an arrow of time analyzed in later sections. Subsequently, a derivation of the laws of thermodynamics from (quantum) statistical mechanics, and, in particular, of the Second Law of thermodynamics, in the forms given to it by Clausius and Carnot, is presented. In a third part, results on diffusive (Brownian) motion of a quantum particle interacting with a quasi-free quantum-mechanical heat bath are reviewed. This is followed by an outline of a theory of friction by emission of Cherenkov radiation of sound waves in a system consisting of a particle moving through a Bose- Einstein condensate and interacting with it. In what may be the most important section of this paper, the fundamental arrow of time inherent in Quantum Mechanics is discussed.

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