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von Neumann, J.L. (1932) Mathematische Grundlagen der Quantenmechanik, Springer, Berlin. In: Beyer, E.T., Ed., (1955) Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton.

has been cited by the following article:

• TITLE: The Mathematical Foundations of Quantum Thermodynamics

  AUTHORS: Akira Suzuki, Hisao Taira

  KEYWORDS: Basic Laws in Thermodynamics, Thermodynamic State Space, Pure and Mixed States, Classical Thermodynamics, Quantum Thermodynamics, Transitive Law, Mixed Ensemble

  JOURNAL NAME: Journal of Modern Physics, Vol.11 No.4, April 8, 2020

  ABSTRACT: It is proposed a representation of the basic laws (i.e. the zeroth, first, second and third laws) in thermodynamics for quantum systems in the pure and mixed ensembles, respectively. We show that the basic laws are represented by parameters that specify respective quantum states. The parameters are the elements of the thermodynamic state space Mθ and the state space Mϑ of the mixed ensemble for quantum systems. The introduction of such parameters is based on a probabilistic nature of quantum theory. Consistency between quantum theory and classical thermodynamics is preserved throughout the formulation for the representation of the thermodynamical laws in quantum systems (quantum thermodynamics). The present theory gives the mathematical foundations of quantum thermodynamics.