Thermodynamic Uncertainty Relation in Interacting Many-Body Systems

TL;DR

This paper investigates the thermodynamic uncertainty relation (TUR) in large interacting many-body systems, providing explicit formulas and demonstrating practical applications in driven lattice gases.

Contribution

It derives an explicit expression for the optimal estimate of entropy production in many-body systems with interactions, extending TUR analysis.

Findings

Explicit formula for entropy production estimate in many-body systems

Demonstration of the approach in driven lattice gas models

Quantitative analysis of TUR in systems with short-range interactions

Abstract

The thermodynamic uncertainty relation (TUR) has been well studied for systems with few degrees of freedom. While, in principle, the TUR holds for more complex systems with many interacting degrees of freedom as well, little is known so far about its behavior in such systems. We analyze the TUR in the thermodynamic limit for mixtures of driven particles with short-range interactions. Our main result is an explicit expression for the optimal estimate of the total entropy production in terms of single-particle currents and correlations between two-particle currents. Quantitative results for various versions of a driven lattice gas demonstrate the practical implementation of this approach.