Anomalous thermodynamics at the micro-scale

TL;DR

This paper reveals that at micro-scales, the commonly used overdamped approximation fails to accurately describe entropy production when temperature gradients are present, due to an entropic anomaly caused by finite inertia effects.

Contribution

It demonstrates the existence of an entropic anomaly at micro-scales, showing that finite inertia significantly impacts entropy production contrary to overdamped models.

Findings

Overdamped approximation fails for entropy in temperature gradients.

Finite inertia causes a dominant anomalous entropy production.

Anomalous entropy is linked to temperature gradient sweeps.

Abstract

Particle motion at the micro-scale is an incessant tug-of-war between thermal fluctuations and applied forces on one side, and the strong resistance exerted by fluid viscosity on the other. Friction is so strong that completely neglecting inertia - the overdamped approximation - gives an excellent effective description of the actual particle mechanics. In sharp contrast with this result, here we show that the overdamped approximation dramatically fails when thermodynamic quantities such as the entropy production in the environment is considered, in presence of temperature gradients. In the limit of vanishingly small, yet finite inertia, we find that the entropy production is dominated by a contribution that is anomalous, i.e. has no counterpart in the overdamped approximation. This phenomenon, that we call entropic anomaly, is due to a symmetry-breaking that occurs when moving to the small, finite inertia limit. Strong production of anomalous entropy is traced back to intense sweeps down the temperature gradient.