Fluctuation relations in non-equilibrium stationary states of Ising models

TL;DR

This paper investigates fluctuation relations in non-equilibrium stationary states of Ising models through Monte Carlo simulations, examining heat exchange and work under various conditions, confirming theoretical predictions and observing finite-time corrections.

Contribution

It provides a comprehensive numerical study of fluctuation relations in Ising models with different driving mechanisms and analyzes finite-time effects.

Findings

Fluctuation relation holds in large time limit for heat exchange.

Finite-time corrections follow a scaling behavior.

Work fluctuations also satisfy the fluctuation relation under shear.

Abstract

Fluctuation relations for the entropy production in non equilibrium stationary states of Ising models are investigated by Monte Carlo simulations. Systems in contact with heat baths at two different temperatures or subject to external driving will be studied. In the first case, by considering different kinetic rules and couplings with the baths, the behavior of the probability distributions of the heat exchanged in a time $\tau$ with the thermostats, both in the disordered and in the low temperature phase, are discussed. The fluctuation relation is always verified in the large $\tau $ limit and deviations from linear response theory are observed. Finite-$\tau$ corrections are shown to obey a scaling behavior. In the other case the system is in contact with a single heat bath but work is done by shearing it. Also for this system the statistics collected for the mechanical work shows the validity of the fluctuation relation and preasymptotic corrections behave analogously to the case with two baths.