Classical and quantum thermodynamics in a non-equilibrium regime: Application to Stirling engine
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913511317176320 |
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| author | Koyanagi, Shoki Tanimura, Yoshitaka |
| author_facet | Koyanagi, Shoki Tanimura, Yoshitaka |
| contents | We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system-bath model [S. Koyanagi and Y. Tanimura, J. Chem. Phys. \textbf{160}, 234112 (2024)]. Based on the dimensionless (DL) minimum work principle, non-equilibrium thermodynamic potentials are expressed in terms of non-equilibrium extensive and intensive variables in time derivative form. This is made possible by incorporating the entropy production rate into the definitions of non-equilibrium thermodynamic potentials. These potentials can be evaluated from the DL non-equilibrium-to-equilibrium minimum work principle, which is derived from the principle of DL minimum work and is equivalent to the second law of thermodynamics. We thus obtain the non-equilibrium Massieu-Planck potentials as entropic potentials and the non-equilibrium Helmholtz-Gibbs potentials as free energies. Unlike fluctuation theorem and stochastic thermodynamics theory, this theory does not require the assumption of a factorized initial condition and is valid in the full quantum regime where the system and bath are quantum mechanically entangled. Our results are numerically verified by simulating a thermostatic Stirling engine consisting of two isothermal processes and two thermostatic processes using the quantum hierarchical Fokker--Planck equations and the classical Kramers equation derived from the thermodynamic system-bath model. We then show that, from weak to strong system-bath interactions, the thermodynamic process can be analyzed using a non-equilibrium work diagram analogous to the equilibrium one for given time-dependent intensive variables. The results can be used to develop efficient heat machines in non-equilibrium regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical and quantum thermodynamics in a non-equilibrium regime: Application to Stirling engine Koyanagi, Shoki Tanimura, Yoshitaka Statistical Mechanics Chemical Physics We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system-bath model [S. Koyanagi and Y. Tanimura, J. Chem. Phys. \textbf{160}, 234112 (2024)]. Based on the dimensionless (DL) minimum work principle, non-equilibrium thermodynamic potentials are expressed in terms of non-equilibrium extensive and intensive variables in time derivative form. This is made possible by incorporating the entropy production rate into the definitions of non-equilibrium thermodynamic potentials. These potentials can be evaluated from the DL non-equilibrium-to-equilibrium minimum work principle, which is derived from the principle of DL minimum work and is equivalent to the second law of thermodynamics. We thus obtain the non-equilibrium Massieu-Planck potentials as entropic potentials and the non-equilibrium Helmholtz-Gibbs potentials as free energies. Unlike fluctuation theorem and stochastic thermodynamics theory, this theory does not require the assumption of a factorized initial condition and is valid in the full quantum regime where the system and bath are quantum mechanically entangled. Our results are numerically verified by simulating a thermostatic Stirling engine consisting of two isothermal processes and two thermostatic processes using the quantum hierarchical Fokker--Planck equations and the classical Kramers equation derived from the thermodynamic system-bath model. We then show that, from weak to strong system-bath interactions, the thermodynamic process can be analyzed using a non-equilibrium work diagram analogous to the equilibrium one for given time-dependent intensive variables. The results can be used to develop efficient heat machines in non-equilibrium regimes. |
| title | Classical and quantum thermodynamics in a non-equilibrium regime: Application to Stirling engine |
| topic | Statistical Mechanics Chemical Physics |
| url | https://arxiv.org/abs/2405.17791 |