Van Vu Tan, Hasegawa Yoshihiko
Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
Phys Rev Lett. 2021 Jan 8;126(1):010601. doi: 10.1103/PhysRevLett.126.010601.
We derive geometrical bounds on the irreversibility in both quantum and classical Markovian open systems that satisfy the detailed balance condition. Using information geometry, we prove that irreversible entropy production is bounded from below by a modified Wasserstein distance between the initial and final states, thus strengthening the Clausius inequality in the reversible-Markov case. The modified metric can be regarded as a discrete-state generalization of the Wasserstein metric, which has been used to bound dissipation in continuous-state Langevin systems. Notably, the derived bounds can be interpreted as the quantum and classical speed limits, implying that the associated entropy production constrains the minimum time of transforming a system state. We illustrate the results on several systems and show that a tighter bound than the Carnot bound for the efficiency of quantum heat engines can be obtained.
我们推导了满足细致平衡条件的量子和经典马尔可夫开放系统中不可逆性的几何界限。利用信息几何，我们证明了不可逆熵产生由初始态和终态之间的修正瓦瑟斯坦距离从下方界定，从而在可逆马尔可夫情形下强化了克劳修斯不等式。修正度量可被视为瓦瑟斯坦度量的离散态推广，其已被用于界定连续态朗之万系统中的耗散。值得注意的是，推导得到的界限可被解释为量子和经典速度极限，这意味着相关的熵产生限制了系统状态转变的最短时间。我们在几个系统上展示了结果，并表明可以得到比量子热机效率的卡诺界限更紧的界限。
