Colloquium: Statistical mechanics and thermodynamics at strong coupling: Quantum and classical

Peter Talkner and Peter Hänggi
Rev. Mod. Phys. 92, 041002 – Published 21 October 2020; Erratum Rev. Mod. Phys. 94, 039901 (2022)

Abstract

The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or the reduced phase-space probability density function of a classical open system, the Hamiltonian of mean force not only characterizes the reduced state but also contains full information about the thermodynamics of the considered open system. The resulting thermodynamic potentials all assume the form as the difference of the potentials for the total system and the bare environment in the absence of the system. In contrast to work as a mechanical notion, one faces several problems with the definition of heat, which turns out to be largely ambiguous in the case of strong coupling between system and environment. The general theory of the thermodynamics of open systems, in particular, in view of strong coupling, is reviewed and illustrated it with several examples. The vagueness of heat is discussed in the context of the ambiguities in the definitions of a fluctuating internal energy and other fluctuating thermodynamic potentials.

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  • Received 18 November 2019

DOI:https://doi.org/10.1103/RevModPhys.92.041002

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Erratum

Authors & Affiliations

Peter Talkner*

  • Institute of Physics, University of Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany and Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34113, Republic of Korea

Peter Hänggi

  • Institute of Physics, University of Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany, Nanosystems Initiative Munich, Schellingstraße 4, D-80799 München, Germany, and Department of Physics, National University of Singapore, Singapore 117546

  • *peter.talkner@physik.uni-augsburg.de
  • hanggi@physik.uni-augsburg.de

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Vol. 92, Iss. 4 — October - December 2020

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