Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes
Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes
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DOI：
10.1103/physrevresearch.5.013217
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发表时间：
2022-08
影响因子：
4.2
通讯作者：
Kazutaka Takahashi;Y. Utsumi
中科院分区：
文献类型：
--
作者：
Kazutaka Takahashi;Y. Utsumi
本文推广了量子系统中由不同生成元演化的两个态之间距离的速度极限[K。Suzuki和K. Takahashi，Phys.Rev.Res.2，032016（R）（2020）]到由主方程描述的经典随机过程。我们证明了任意演化状态之间的迹距离是有界的从上面使用的几何度量。几何约束减少到Fisher信息度量之间的时间演化状态和初始状态的距离。我们比较了在松弛和退火过程中的约束与已知的非平衡热力学系统的不同类型的约束。对于退火和抽运过程等动力学过程，时间演化态和瞬时定态之间的距离是一个合适的选择，定态的Fisher信息度量表示其上界.度规与从定态的时间依赖性定义的反绝热项有关。
We extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)] to the classical stochastic processes described by the master equation. We demonstrate that the trace distance between arbitrary evolving states is bounded from above by using a geometrical metric. The geometrical bound reduces to the Fisher information metric for the distance between the time-evolved state and the initial state. We compare the bound in relaxation and annealing processes with a different type of bound known for nonequilibrium thermodynamical systems. For dynamical processes such as annealing and pumping processes, the distance between the time-evolved state and the instantaneous stationary state becomes a proper choice and the bound is represented by the Fisher information metric of the stationary state. The metric is related to the counterdiabatic term defined from the time dependence of the stationary state.