Author(s)

Akira Suzuki¹, Hisao Taira²

¹Faculty of Science, Tokyo University of Science, Shinjyuku-Ku, Tokyo, Japan.
²Faculty of Education, Hokkaido University of Education, Kita-Ku, Sapporo, Japan.

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 M_θ and the state space M_ϑ 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.

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

Suzuki, A. and Taira, H. (2020) The Mathematical Foundations of Quantum Thermodynamics. Journal of Modern Physics, 11, 517-527. doi: 10.4236/jmp.2020.114034.