马尔可夫动力学相对熵的非凸性：Fisher信息方法
Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach
摘要：
通过反例证明了马尔可夫主方程解与稳态解之间的相对熵不是时间的凸函数。因此，我们放下帷幕上的热力学原理的一个可能的制定有关的非绝热熵产生的减少。然而，我们认为，一个大的分离的典型的衰减时间是必要的非凸的解决方案发生，凹瞬态非常短暂的主要松弛模式。我们描述了一种基于Fisher信息矩阵的通用方法来区分允许和不允许非凸解的生成器。虽然导致凹瞬态的初始条件被证明是非常精细的调整，通过我们的方法，我们能够选择任意接近稳态的非凸初始条件。当系统接近于满足细致平衡时，或者更一般地说，当满足衰减模式的某些正态性条件时，凸性确实发生。我们的结果限制了Maes等人提出的猜想的有效性范围。107，010601（2011）]关于占用概率（动态活动）的大偏差率泛函的单调性，表明虽然猜想可能在长时间限制下仍然成立，但动态活动不是李雅普诺夫函数。
英文摘要：
We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus let down a curtain on a possible formulation of a principle of thermodynamics regarding decrease of the nonadiabatic entropy production. However, we argue that a large separation of typical decay times is necessary for nonconvex solutions to occur, making concave transients extremely short-lived with respect to the main relaxation modes. We describe a general method based on the Fisher information matrix to discriminate between generators that do and don't admit nonconvex solutions. While initial conditions leading to concave transients are shown to be extremely fine-tuned, by our method we are able to select nonconvex initial conditions that are arbitrarily close to the steady state. Convexity does occur when the system is close to satisfy detailed balance, or more generally when certain normality conditions of the decay modes are satisfied. Our results circumscribe the range of validity of a conjecture proposed by Maes et al. [Phys. Rev. Lett. 107, 010601 (2011)] regarding monotonicity of the large deviation rate functional for the occupation probability (dynamical activity), showing that while the conjecture might still hold in the long time limit, the dynamical activity is not a Lyapunov function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
