Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes

TL;DR

This paper generalizes speed limits for classical stochastic systems using a geometrical metric, linking it to Fisher information and applying it to relaxation, annealing, and pumping processes.

Contribution

It extends quantum speed limits to classical stochastic processes and introduces a geometrical bound based on Fisher information for various dynamical systems.

Findings

The trace distance is bounded by a geometrical metric.

The bound reduces to Fisher information metric for certain states.

Application to relaxation, annealing, and pumping processes.

Abstract

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.