Shi Zeyi, Abe Sumiyoshi
Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
Institute of Physics, Kazan Federal University, Kazan 420008, Russia.
Entropy (Basel). 2020 Oct 26;22(11):1219. doi: 10.3390/e22111219.
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini-Kossakowski-Lindblad-Sudarshan equation.
弱不变量是具有守恒期望值的时间相关可观测量。然而，它们的涨落并不随时间保持恒定。假设开放量子系统状态的时间演化由完全正映射给出，即使该映射不是幺正的，涨落也会单调增长，这与冯·诺依曼熵和雷尼熵的单调增加都要求映射是幺正的这一事实形成对比。通过这种方式，弱不变量以一种不同于熵的方式描述了时间不对称性。给出了在系统密度矩阵服从戈里尼 - 科萨克夫斯基 - 林德布拉德 - 苏达山方程的情况下，与弱不变量相关的协方差矩阵的时间演化公式。
