A system–bath (SB) model is considered to examine the Jarzynski equality in the fully quantum regime. In our previous paper [J. Chem. Phys. 153, 234107 (2020)], we carried out “exact” numerical experiments using hierarchical equations of motion (HEOM) in which we demonstrated that the SB model describes behavior that is consistent with the first and second laws of thermodynamics and that the dynamics of the total system are time irreversible. The distinctive quantity in the Jarzynski equality is the “work characteristic function (WCF)”, 〈exp[−βW]〉, where W is the work performed on the system and β is the inverse temperature. In the present investigation, we consider the definitions based on the partition function (PF) and on the path, and numerically evaluate the WCF using the HEOM to determine a method for extending the Jarzynski equality to the fully quantum regime. We show that using the PF-based definition of the WCF, we obtain a result that is entirely inconsistent with the Jarzynski equality, while if we use the path-based definition, we obtain a result that approximates the Jarzynski equality, but may not be consistent with it.

中文翻译：

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非平衡功的开放量子动力学理论：运动方法的层次方程

考虑使用系统浴（SB）模型来检查全量子状态下的Jarzynski等式。在我们以前的论文[J. 化学 物理 153，234107（2020）]，我们进行了“精确”的数值实验使用其中我们表明，SB模型描述的行为是热力学第一和第二定律一致运动（HEOM）的分层方程和动力学整个系统是时间不可逆的。Jarzynski等式中的特征量是“功特征函数（WCF）”，〈exp [ -βW ]〉，其中W是在系统上执行的功，β是是逆温度。在本研究中，我们考虑基于分配函数（PF）和路径的定义，并使用HEOM对WCF进行数值评估，以确定将Jarzynski等式扩展到全量子态的方法。我们表明，使用WCF的基于PF的定义，我们得到的结果与Jarzynski等式完全不一致，而如果使用基于路径的定义，则我们得到的结果近似于Jarzynski相等，但可能不是与之一致。