%0 Journal Article
%T The Mathematical Foundations of Quantum Thermodynamics
%A Akira Suzuki
%A Hisao Taira
%J Journal of Modern Physics
%P 517-527
%@ 2153-120X
%D 2020
%I Scientific Research Publishing
%R 10.4236/jmp.2020.114034
%X It is proposed a representation of the basic laws (<em>i.e.</em> 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<span style=\"white-space:nowrap;\"><sub><em>&amp;theta;</em></sub></span> and the state space M<span style=\"white-space:nowrap;\"><sub><em>&amp;thetasym;</em></sub></span> 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.
%K Basic Laws in Thermodynamics
%K Thermodynamic State Space
%K Pure and Mixed States
%K Classical Thermodynamics
%K Quantum Thermodynamics
%K Transitive Law
%K Mixed Ensemble
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=99377