{"title":"非平衡状态下的经典和量子热力学:热静力斯特林发动机的应用","authors":"Shoki Koyanagi, Yoshitaka Tanimura","doi":"10.1063/5.0220685","DOIUrl":null,"url":null,"abstract":"We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system–bath model [Koyanagi and Tanimura, J. Chem. Phys. 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 definition 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 the 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.","PeriodicalId":501648,"journal":{"name":"The Journal of Chemical Physics","volume":"40 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classical and quantum thermodynamics in a non-equilibrium regime: Application to thermostatic Stirling engine\",\"authors\":\"Shoki Koyanagi, Yoshitaka Tanimura\",\"doi\":\"10.1063/5.0220685\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system–bath model [Koyanagi and Tanimura, J. Chem. Phys. 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 definition 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 the 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. 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引用次数: 0
摘要
我们开发了一种非平衡态热力学理论,并将其描述为热力学系统-浴模型[Koyanagi and Tanimura, J. Chem. Phys. 160, 234112 (2024)]。根据无量纲(DL)最小功原理,非平衡热力学势可以用时间导数形式的非平衡广泛变量和密集变量来表示。通过将熵产生率纳入非平衡热力学势的定义,这一点成为可能。这些势能可根据 DL 非平衡到平衡最小功原理进行评估,该原理源于 DL 最小功原理,等同于热力学第二定律。因此,我们可以得到作为熵势的非平衡马修-普朗克势和作为自由能的非平衡亥姆霍兹-吉布斯势。与波动定理和随机热力学理论不同的是,该理论不需要假设因子化初始条件,并且在系统和浴槽量子力学纠缠的全量子体系中有效。我们利用量子分层福克-普朗克方程和从热力学系统-浴模型中推导出的经典克拉默方程,模拟了一台由两个等温过程和两个恒温过程组成的恒温斯特林发动机,从数值上验证了我们的结果。然后我们证明,从弱系统-水浴相互作用到强系统-水浴相互作用,热力学过程都可以使用非平衡功图进行分析,类似于给定时间相关密集变量的平衡功图。这些结果可用于开发非平衡状态下的高效热机。
Classical and quantum thermodynamics in a non-equilibrium regime: Application to thermostatic Stirling engine
We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system–bath model [Koyanagi and Tanimura, J. Chem. Phys. 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 definition 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 the 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.