Excess and loss of entropy production for different levels of coarse-graining

TL;DR

This paper examines how different levels of coarse-graining, including underdamped, overdamped, and Markov chain approximations, affect entropy production estimates in a driven colloidal system, revealing regimes of excess and loss.

Contribution

It introduces a systematic analysis of entropy production under various coarse-graining levels, highlighting the impact of inertia and discretization on energetic properties.

Findings

Overdamped approximation can overestimate entropy production at moderate viscosities.

Inertia induces multiple jumps affecting entropy calculations.

Discretization via Markov chains captures key dynamics across coarse-graining levels.

Abstract

We investigate the effect of coarse-graining on the energetics properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a sinusoidal potential and driven out of equilibrium by a small constant force. Different levels of coarse-graining are evaluated: at first, we compare the results in the underdamped dynamics with those in the overdamped one (first coarse-graining). For large values of the viscosity, the two dynamics have the same energetic properties, while, for smaller viscosity values, the overdamped approximation produces an excess of entropy production with respect to that of the underdamped dynamics. Moreover, for further smaller values of the drag coefficient, the excess of entropy production turns into a loss. These regimes are explained by evaluating the jump statistics, observing that the inertia is able to induce multiple jumps and affect the average jump rate. The periodic shape of the potential allows us to approximate the continuous dynamics via a Markov chain, after the introduction of a suitable time and space discretization (second level of coarse-graining). This discretization procedure is implemented starting both from the underdamped and the overdamped evolution and is analyzed for different values of the viscosity.