Geometric decomposition of entropy production in out-of-equilibrium systems

TL;DR

This paper introduces a geometric framework to decompose entropy production in out-of-equilibrium systems into excess and housekeeping parts, enabling independent calculation from trajectory data.

Contribution

It provides a novel geometric formulation and variational expressions for entropy contributions, distinguishing different types of driving forces in non-equilibrium systems.

Findings

Derived orthogonal contributions to system currents from geometric decomposition

Developed variational formulas for excess and housekeeping entropy

Applied method to particle in a time-dependent tilted periodic potential

Abstract

Two qualitatively different ways of driving a physical system out of equilibrium, time-dependent and non-conservative forcing, are reflected by the decomposition of the system's entropy production into excess and housekeeping parts. We show that the difference between these two types of driving gives rise to a geometric formulation in terms of two orthogonal contributions to the currents in the system. This geometric picture in a natural way leads to variational expressions for both the excess and housekeeping entropy, which allow calculating both contributions independently from the trajectory data of the system. We demonstrate this by calculating the excess and housekeeping entropy of a particle in a time-dependent, tilted periodic potential.