The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems that are those systems for which sub-systems are out of consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians –which are absent in undecomposed systems– can be a source of irreversibility in decomposed systems. Thus, the following two-stage task arises: How to modify von Neumann’s equation of undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems? The first step was already done in Muschik (“Concepts of phenomenological irreversible quantum thermodynamics: closed undecomposed Schottky systems in semi-classical description,” J. Non-Equilibrium Thermodyn., vol. 44, pp. 1–13, 2019) and is repeated below, whereas the second step to formulate a quantum thermodynamics of decomposed systems is performed here by modifying the von Neumann equations of the sub-systems by a procedure wich is similar to that of Lindblad’s equation (G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys., vol. 48, p. 119130, 1976), but different because the sub-systems interact with one another through partitions.

中文翻译：

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现象学不可逆量子热力学的概念 II：二分系统的时间相关统计系综

广为流传的观点是，原始量子力学是一个可逆理论，但这种说法只适用于未分解的系统，即未考虑子系统的系统。考虑到子系统，因为根据定义它是分解系统所必需的，相互作用哈密顿量——在未分解系统中不存在——可能是分解系统不可逆性的来源。因此，出现了以下两个阶段的任务：如何修改未分解系统的冯·诺依曼方程以使其出现不可逆性，以及这种修改如何影响分解系统？Muschik 已经完成了第一步（“现象学不可逆量子热力学的概念：半经典描述中的封闭未分解肖特基系统，”J. 非平衡热力学。，卷。44, pp. 1-13, 2019) 并在下面重复，而此处的第二步是通过类似于Lindblad 方程（G. Lindblad，“关于量子动力学半群的生成元，”公社。数学。物理。，卷。48 页 119130, 1976)，但不同之处在于子系统通过分区相互交互。