Clarke Claudia L, Ford Ian J
Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Phys Rev E. 2023 Jul;108(1-1):014129. doi: 10.1103/PhysRevE.108.014129.
Irreversible behavior in open stochastic dynamical systems is quantified by stochastic entropy production, a property that measures the difference in likelihoods of forward and subsequent backward system evolution. But for a closed system, governed by deterministic dynamics, such an approach is not appropriate. Instead, we can consider the difference in likelihoods of forward and "obverse" behavior: the latter being a backward trajectory initiated at the same time as the forward trajectory. Such a comparison allows us to define "dissipation production," an analog of stochastic entropy production. It quantifies the breakage of a property of the evolution termed "obversibility" just as stochastic entropy production quantifies a breakage of reversibility. Both are manifestations of irreversibility. In this study we discuss dissipation production in a quantum system. We consider a simple, deterministic, two-level quantum system characterized by a statistical ensemble of state vectors, and we provide numerical results to illustrate the ideas. We consider cases that both do and do not satisfy an Evans-Searles Fluctuation Theorem for the dissipation production, and hence identify conditions under which the system displays time-asymmetric average behavior: an arrow of time.
开放随机动力系统中的不可逆行为是通过随机熵产生来量化的，随机熵产生是一种衡量系统正向演化与随后反向演化可能性差异的属性。但对于由确定性动力学支配的封闭系统，这种方法并不适用。相反，我们可以考虑正向行为与“反向行为”可能性的差异：后者是与正向轨迹同时开始的反向轨迹。这种比较使我们能够定义“耗散产生”，它是随机熵产生的类似物。它量化了被称为“反向可逆性”的演化属性的破坏，就像随机熵产生量化了可逆性的破坏一样。两者都是不可逆性的表现。在本研究中，我们讨论量子系统中的耗散产生。我们考虑一个由态矢量统计系综表征的简单、确定性二能级量子系统，并提供数值结果来说明这些概念。我们考虑了满足和不满足关于耗散产生的埃文斯 - 塞尔尔斯涨落定理的情况，从而确定系统显示时间不对称平均行为（时间箭头）的条件。
