Entropic Distance for Nonlinear Master Equation

TL;DR

This paper introduces an entropic distance measure tailored for nonlinear master equations with unidirectional stochastic processes and rare resets, linking it to Tsallis entropy and exploring applications in statistical physics.

Contribution

It demonstrates that nonlinearities in the master equation naturally lead to Tsallis q-entropy, providing a new perspective on entropy maximization in non-equilibrium systems.

Findings

Power-like nonlinearity yields Tsallis q-entropy in stationary states

The entropic distance measure is suitable for systems with unidirectional stochastic processes

Applications to statistical physics phenomena are proposed

Abstract

More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics. We demonstrate that a power-like nonlinearity in the state probability in the master equation naturally leads to the Tsallis (Havrda-Charv\'at, Acz\'el-Dar\'oczy) q-entropy formula in the context of seeking for the maximal entropy state at stationarity. A few possible applications of a certain simple and linear master equation to phenomena studied in statistical physics are listed at the end.