We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system–bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu–Planck potentials as entropic potentials and the Helmholtz–Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker–Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system–bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions.
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Classical and quantum thermodynamics described as a system–bath model: The dimensionless minimum work principle
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21 June 2024
Research Article|
June 21 2024
Classical and quantum thermodynamics described as a system–bath model: The dimensionless minimum work principle
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Shoki Koyanagi
;
Shoki Koyanagi
a)
(Formal analysis, Investigation, Software)
Department of Chemistry, Graduate School of Science, Kyoto University
, Kyoto 606-8502, Japan
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Yoshitaka Tanimura
Yoshitaka Tanimura
a)
(Conceptualization, Formal analysis, Funding acquisition, Investigation, Supervision, Writing – review & editing)
Department of Chemistry, Graduate School of Science, Kyoto University
, Kyoto 606-8502, Japan
Search for other works by this author on:
Department of Chemistry, Graduate School of Science, Kyoto University
, Kyoto 606-8502, Japan
Yoshitaka Tanimura
Conceptualization, Formal analysis, Funding acquisition, Investigation, Supervision, Writing – review & editing
a)
Department of Chemistry, Graduate School of Science, Kyoto University
, Kyoto 606-8502, Japan
J. Chem. Phys. 160, 234112 (2024)
Article history
Received:
February 28 2024
Accepted:
May 23 2024
Citation
Shoki Koyanagi, Yoshitaka Tanimura; Classical and quantum thermodynamics described as a system–bath model: The dimensionless minimum work principle. J. Chem. Phys. 21 June 2024; 160 (23): 234112. https://doi.org/10.1063/5.0205771
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