Entropy production for coarse-grained dynamics

TL;DR

This paper investigates how coarse-grained models like Fokker-Planck equations capture entropy production in non-equilibrium systems and identifies the hidden microscopic currents they miss.

Contribution

It derives analytical expressions for coarse-graining corrections to entropy production, revealing limits of information loss when transitioning from Master Equations to Fokker-Planck equations.

Findings

Coarse-grained entropy production contains hidden microscopic current information.

Analytical formulas for coarse-graining corrections are derived for discrete and continuous systems.

Results can be experimentally verified to infer microscopic processes.

Abstract

Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master Equation that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We show that the corresponding coarse-grained entropy production contains information on microscopic currents that are not captured by the Fokker-Planck equation and thus cannot be deduced from it. We study a discrete-state and a continuous-state system, deriving in both the cases an analytical expression for the coarse-graining corrections to the entropy production. This result elucidates the limits in which there is no loss of information in passing from a Master Equation to a Fokker-Planck equation describing the same system. Our results are amenable of experimental verification, which could help to infer some information about the underlying microscopic processes.