Entropy production in exactly solvable systems

TL;DR

This paper reviews entropy production in exactly solvable stochastic systems, providing explicit calculations across various models to serve as benchmarks and foundations for studying more complex non-equilibrium systems.

Contribution

It offers a comprehensive, self-contained review with explicit entropy production calculations in a variety of exactly solvable models, filling a gap in illustrative examples.

Findings

Explicit entropy production formulas derived for multiple models

Benchmark examples for non-equilibrium stochastic systems

Foundation for analyzing complex active matter systems

Abstract

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.