Work distribution functions for hysteresis loops in a single-spin system

TL;DR

This paper investigates the distribution of work done on a single Ising spin under a time-dependent magnetic field, using simulations and analytical methods to explore fluctuation theorems and work characteristics.

Contribution

It provides a detailed analysis of work distributions in a single-spin system under various driving rates, including verification of fluctuation theorems.

Findings

Work distributions are broad with negative dissipated work probability.

Fluctuation theorems hold for equilibrium initial states.

Steady state fluctuation theorem is not satisfied.

Abstract

We compute the distribution of the work done in driving a single Ising spin with a time-dependent magnetic field. Using Glauber dynamics we perform Monte-Carlo simulations to find the work distributions at different driving rates. We find that in general the work-distributions are broad with a significant probability for processes with negative dissipated work. The special cases of slow and fast driving rates are studied analytically. We verify that various work fluctuation theorems corresponding to equilibrium initial states are satisfied while a steady state version is not.