Non-equilibrium and information: the role of cross-correlations

TL;DR

This paper explores how cross-correlations in non-equilibrium systems influence entropy production and fluctuation-dissipation theorem violations, highlighting the importance of considering coupled degrees of freedom for accurate modeling.

Contribution

It demonstrates the impact of neglecting or simplifying cross-correlations in reduced models on entropy production and response functions in non-equilibrium systems.

Findings

Ignoring coupling leads to discrepancies in entropy production and response.

Generalized Langevin models reproduce linear response but lose entropy production information.

Linear force systems show significant entropy loss, complicating FDT violation interpretation.

Abstract

We discuss the relevance of information contained in cross-correlations among different degrees of freedom, which is crucial in non-equilibrium systems. In particular we consider a stochastic system where two degrees of freedom $X_1$ and $X_2$ - in contact with two different thermostats - are coupled together. The production of entropy and the violation of equilibrium fluctuation-dissipation theorem (FDT) are both related to the cross-correlation between $X_1$ and $X_2$. Information about such cross-correlation may be lost when single-variable reduced models, for $X_1$, are considered. Two different procedures are typically applied: (a) one totally ignores the coupling with $X_2$; (b) one models the effect of $X_2$ as an average memory effect, obtaining a generalized Langevin equation. In case (a) discrepancies between the system and the model appear both in entropy production and linear response; the latter can be exploited to define effective temperatures, but those are meaningful only when time-scales are well separated. In case (b) linear response of the model well reproduces that of the system; however the loss of information is reflected in a loss of entropy production. When only linear forces are present, such a reduction is dramatic and makes the average entropy production vanish, posing problems in interpreting FDT violations.