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

Shoki Koyanagi; Yoshitaka Tanimura

doi:10.1063/5.0205771

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arXiv · 2405.16787

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

Shoki Koyanagi·Yoshitaka Tanimura

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Abstract

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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Shoki Koyanagi, Yoshitaka Tanimura. 2024-05-27. Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle. https://doi.org/10.1063/5.0205771

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