Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle

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Main Authors: Koyanagi, Shoki, Tanimura, Yoshitaka
Format: Preprint
Published: 2024
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author Koyanagi, Shoki
Tanimura, Yoshitaka
author_facet Koyanagi, Shoki
Tanimura, Yoshitaka
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_16787
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle
Koyanagi, Shoki
Tanimura, Yoshitaka
Statistical Mechanics
Chemical Physics
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.
title Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle
topic Statistical Mechanics
Chemical Physics
url https://arxiv.org/abs/2405.16787