Lower bound for entropy production rate in stochastic systems far from equilibrium

TL;DR

This paper establishes a lower bound for entropy production in nonequilibrium stochastic systems, linking thermodynamics with graph theory, and provides a tighter inequality for divergence measures under involutions.

Contribution

It introduces a lower bound for entropy production rate based on Markov graph weights and proves a tight bound for Kullback-Leibler divergence under involutions, improving existing inequalities.

Findings

Lower bound for entropy production rate in terms of graph currents

Tight lower bound for Kullback-Leibler divergence under involutions

Connection between nonequilibrium thermodynamics and graph theory

Abstract

We show that the Schnakenberg's entropy production rate in a master equation is lower bounded by a function of the weight of the Markov graph, here defined as the sum of the absolute values of probability currents over the edges. The result is valid for time-dependent nonequilibrium entropy production rates. Moreover, in a general framework, we prove a theorem showing that the Kullback-Leibler divergence between distributions $P(s)$ and $P'(s):=P(m(s))$, where $m$ is an involution, $m(m(s))=s$, is lower bounded by a function of the total variation of $P$ and $P'$, for any $m$. The bound is tight and it improves on Pinsker's inequality for this setup. This result illustrates a connection between nonequilibrium thermodynamics and graph theory with interesting applications.