Hidden entropy production by fast variables

TL;DR

This paper studies nonequilibrium entropy production in coupled Brownian particles, revealing that fast variables can hide additional entropy production not apparent in the slow variables, especially as the coupling strength increases.

Contribution

It demonstrates that fast variables contribute hidden entropy production in harmonic systems, even in the strong coupling limit, contrasting with rigid rod models.

Findings

Harmonic systems produce more entropy than rigid rods at large coupling K.

Fast variables contribute significantly to total entropy production.

Hidden entropy production persists in the K→∞ limit due to fast degrees of freedom.

Abstract

We investigate nonequilibrium underdamped Langevin dynamics of Brownian particles that interact through a harmonic potential with coupling constant $K$ and are in thermal contact with two heat baths at different temperatures. The system is characterized by a net heat flow and an entropy production in the steady state. We compare the entropy production of the harmonic system with that of Brownian particles linked with a rigid rod. The harmonic system may be expected to reduce to the rigid rod system in the infinite $K$ limit. However, we find that the harmonic system in the $K\to\infty$ limit produces more entropy than the rigid rod system. The harmonic system has the center of mass coordinate as a slow variable and the relative coordinate as a fast variable. By identifying the contributions of the degrees of freedom to the total entropy production, we show that the hidden entropy production by the fast variable is responsible for the extra entropy production. We discuss the $K$ dependence of each contribution.