论文标题
马尔可夫系统中不可逆性的几何界限
Geometrical Bounds of the Irreversibility in Markovian Systems
论文作者
论文摘要
我们在满足详细平衡条件的量子和经典的马尔可夫开放系统的不可逆性上得出了几何界限。使用信息几何形状，我们证明了不可逆的熵产生是从下面的，在初始状态和最终状态之间的修改后距离，从而增强了可逆 - 马尔科夫案中的克劳西乌斯不平等。修改后的度量可以被视为Wasserstein度量标准的离散状态概括，该公制已用于在连续状态Langevin系统中结合耗散。值得注意的是，派生的边界可以解释为量子和经典速度限制，这意味着相关的熵产生限制了转换系统状态的最小时间。我们说明了几个系统上的结果，并表明可以获得比Carnot结合的紧密结合，以获得量子热发动机的效率。
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.
