Speed Limit for Classical Stochastic Processes

TL;DR

This paper establishes fundamental speed limits for classical stochastic Markov processes, linking the transformation speed to entropy production and dynamical activity, with improved bounds for systems with stationary currents.

Contribution

It introduces new trade-off inequalities that connect the speed of state transformations with entropy production and dynamical activity, providing clear physical interpretations.

Findings

Existence of a trade-off inequality between speed and entropy production.

Dynamical activity influences the time scale of processes.

Stronger bounds are derived for systems with stationary current.

Abstract

Speed limit for classical stochastic Markov processes with discrete states is studied. We find that a trade-off inequality exists between the speed of the state transformation and the entropy production. The dynamical activity determines the time scale and plays a crucial role in the inequality. For systems with stationary current, a similar trade-off inequality with the Hatano-Sasa entropy production gives a much better bound on the speed of the state transformation. Our inequalities contain only physically well-defined quantities, and thus the physical picture of these inequalities is clear.