Entropy production in linear Langevin systems

TL;DR

This paper derives exact formulas for entropy production and related quantities in linear Langevin systems with mixed variables, providing tools for analyzing large-scale stochastic systems and illustrating them with electrical circuit examples.

Contribution

It introduces exact formulas for entropy-related quantities in linear Langevin systems with mixed variables, enabling large-scale analysis and practical applications.

Findings

Exact formulas for entropy production rate and flux derived

Formulas applicable to large-scale systems

Application demonstrated on electrical circuits

Abstract

We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem.