Entropy rate of random walks on complex networks under stochastic resetting

TL;DR

This paper investigates how stochastic resetting influences the entropy rate of random walks on complex networks, revealing nonmonotonic behavior and an optimal resetting probability that maximizes entropy.

Contribution

It introduces the analysis of entropy rate dependence on resetting probability in complex network random walks, showing nontrivial effects and the possibility of exceeding maximal-entropy walks.

Findings

Entropy rate exhibits nonmonotonic dependence on resetting probability.

An optimal resetting probability maximizes the entropy rate.

Maximum entropy rate can surpass that of maximal-entropy random walks.

Abstract

Stochastic processes under resetting at random times have attracted a lot of attention in recent years and served as illustrations of nontrivial and interesting static and dynamic features of stochastic dynamics. In this paper, we aim to address how the entropy rate is affected by stochastic resetting in discrete-time Markovian processes, and explore nontrivial effects of the resetting in the mixing properties of a stochastic process. In particular, we consider resetting random walks on complex networks and compute the entropy rate as a function of the resetting probability. Interestingly, we find that the entropy rate can show a nonmonotonic dependence on the resetting probability. There exists an optimal resetting probability for which the entropy rate reaches a maximum. We also show that the maximum entropy rate can be larger than that of the maximal-entropy random walks on the same topology. Our study provides a new nontrivial effect of stochastic resetting on nonequilibrium statistical physics.