Abstract
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.
References
[1] W. Muschik and M. Kaufmann, Quantum-thermodynamical description of discrete non-equilibrium systems, J. Non-Equilib. Thermodyn. 19 (1994), 76–94.10.1515/jnet.1994.19.1.76Search in Google Scholar
[2] W. Schottky, Thermodynamik, Springer, Berlin, 1929, Erster Teil § 1.10.1007/978-3-642-88482-5_1Search in Google Scholar
[3] W. Muschik, Aspects of Non-Equilibrium Thermodynamics, World Scientific, Singapore, 1990, Chap. 1.1.10.1142/0991Search in Google Scholar
[4] W. Muschik, Second law and non-equilibrium entropy of Schottky systems —Doubts and verification–, Entropy 20 (2018), no. 740, 1–15.10.3390/e20100740Search in Google Scholar
[5] W. Muschik, Empirical foundation and axiomatic treatment of non-equilibrium temperature, Arch. Ration. Mech. Anal. 66 (1977), 379–401.10.1007/BF00248902Search in Google Scholar
[6] W. Muschik and G. Brunk, A concept of non-equilibrium temperature, Int. J. Eng. Sci. 15 (1977), 377–389.10.1016/0020-7225(77)90047-7Search in 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. 5.1.10.1007/978-3-7091-4321-6Search in Google Scholar
[8] A. Katz, Principles of Statistical Mechanics, Freeman, San Francisco, 1967.Search in Google Scholar
[9] See [8] Chap. 3, Sect. 8.Search in Google Scholar
[10] W. Muschik and A. Berezovski, Thermodynamic interaction between two discrete systems in non-equilibrium, J. Non-Equilib. Thermodyn. 29 (2004), 237–255.10.1515/JNETDY.2004.053Search in 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), 133–145.10.3176/phys.math.2007.2.09Search in Google Scholar
[12] W. Muschik, Contact quantities and non-equilibrium entropy of discrete systems, J. Non-Equilib. Thermodyn. 34 (2009), 75–92.10.1515/JNETDY.2009.005Search in 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.Search in Google Scholar
[14] W. Muschik, Contact temperature and internal variables: A glace back, 20 years later, J. Non-Equilib. Thermodyn. 39 (2014), 113–121.10.1515/jnet-2014-0016Search in 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.Search in Google Scholar
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