# Frenetic bounds on the entropy production

## TL;DR

This paper establishes bounds on entropy production in stochastic systems using dynamical activity, linking thermodynamic quantities to system dynamics and extending recent uncertainty relations.

## Contribution

It introduces new bounds on entropy production based on dynamical activity and extends uncertainty relations to underdamped diffusions.

## Key findings

- Expected entropy production rate is bounded by dynamical activity.
- Lower bounds on free energy decrease are derived under global detailed balance.
- Extended entropy production bounds to underdamped diffusions.

## Abstract

We show that under local detailed balance the expected entropy production rate is always bounded in terms of the dynamical activity. The activity refers to the time-symmetric contribution in the action functional for path-space probabilities and relates to escape rates and unoriented traffic. Under global detailed balance we get a lower bound on the decrease of free energy which is known from gradient flow analysis. For stationary driven systems we recover some of the recently studied "uncertainty" relations for the entropy production, appearing in studies about the effectiveness of mesoscopic machines and that refine the positivity of the entropy production rate by providing lower bounds in terms of a positive and even function of the current(s). We extend these lower bounds for the entropy production rate to include underdamped diffusions.