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Journal of Non-Equilibrium Thermodynamics

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Concepts of Phenomenological Irreversible Quantum Thermodynamics I: Closed Undecomposed Schottky Systems in Semi-Classical Description

Wolfgang Muschik
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  • Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
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Published Online: 2018-12-06 | DOI: https://doi.org/10.1515/jnet-2018-0087


If the von Neumann equation is modified by time dependent statistical weights, the time rate of entropy, the entropy exchange and the production of a Schottky system are derived whose Hamiltonian does not contain the interaction with the system’s environment. This interaction is semi-classically described by the quantum theoretical expressions of power and entropy exchange.

Keywords: quantum thermodynamics; Schottky systems; semi-classical description


  • [1]

    W. Muschik and M. Kaufmann, Quantum-thermodynamical description of discrete non-equilibrium systems, J. Non-Equilib. Thermodyn. 19 (1994), 76–94.Google Scholar

  • [2]

    W. Schottky, Thermodynamik, Springer, Berlin, 1929, Erster Teil § 1.Google Scholar

  • [3]

    W. Muschik, Aspects of Non-Equilibrium Thermodynamics, World Scientific, Singapore, 1990, Chap. 1.1.Google Scholar

  • [4]

    W. Muschik, Second law and non-equilibrium entropy of Schottky systems —Doubts and verification–, Entropy 20 (2018), no. 740, 1–15.Google Scholar

  • [5]

    W. Muschik, Empirical foundation and axiomatic treatment of non-equilibrium temperature, Arch. Ration. Mech. Anal. 66 (1977), 379–401.Google Scholar

  • [6]

    W. Muschik and G. Brunk, A concept of non-equilibrium temperature, Int. J. Eng. Sci. 15 (1977), 377–389.Google Scholar

  • [7]

    W. Muschik, Fundamentals of non-equilibrium thermodynamics, in: W. Muschik (Ed.), Non-Equilibrium Thermodynamics with Application to Solids, CISM Courses and Lectures 336, Springer, Wien (1993), 1–63, Chap. 5.1.Google Scholar

  • [8]

    A. Katz, Principles of Statistical Mechanics, Freeman, San Francisco, 1967.Google Scholar

  • [9]

    See [8] Chap. 3, Sect. 8.

  • [10]

    W. Muschik and A. Berezovski, Thermodynamic interaction between two discrete systems in non-equilibrium, J. Non-Equilib. Thermodyn. 29 (2004), 237–255.Google Scholar

  • [11]

    W. Muschik and A. Berezovski, Non-equilibrium contact quantities and compound deficiency at interfaces between discrete systems, Proc. Est. Acad. Sci., Phys. Math. 56 (2007), 133–145.Google Scholar

  • [12]

    W. Muschik, Contact quantities and non-equilibrium entropy of discrete systems, J. Non-Equilib. Thermodyn. 34 (2009), 75–92.Google Scholar

  • [13]

    W. Muschik, Contact temperature as an internal variable of discrete systems in non-equilibrium, in: H. Altenbach, J. Pouget, M. Rousseau, B. Collet and T. Michelitsch (Eds.), Generalized Models and Non-Classical Approaches in Complex Materials 1, Springer Nature (2018), 605–618.Google Scholar

  • [14]

    W. Muschik, Contact temperature and internal variables: A glace back, 20 years later, J. Non-Equilib. Thermodyn. 39 (2014), 113–121.Google Scholar

  • [15]

    W. Muschik, Derivation of Gibbs’ fundamental equations by dissipation inequalities (algebraic approach), in: W.-z. Chien (Ed.), Proceedings of the International Conference on Nonlinear Mechanics, Shanghai 29.10.85, 155–162.

About the article

Received: 2018-11-19

Accepted: 2018-11-19

Published Online: 2018-12-06

Citation Information: Journal of Non-Equilibrium Thermodynamics, ISSN (Online) 1437-4358, ISSN (Print) 0340-0204, DOI: https://doi.org/10.1515/jnet-2018-0087.

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