Stochastic Thermodynamics of Micromagnetics

TL;DR

This paper develops a stochastic thermodynamics framework for micro-magnetic systems by extending the Landau-Lifshitz equation with noise, analyzing thermodynamic laws, and verifying fluctuation theorems through simulations.

Contribution

It introduces a stochastic Landau-Lifshitz equation that obeys detailed balance and establishes thermodynamic laws and fluctuation theorems for micro-magnetics.

Findings

The stochastic Landau-Lifshitz equation converges to equilibrium.

Thermodynamic laws are formulated at trajectory and ensemble levels.

Fluctuation theorems are verified numerically.

Abstract

In this work, we study the stochastic thermodynamics of micro-magnetic systems. We first formulate the stochastic dynamics of micro-magnetic systems by incorporating noises into Landau-Lifshitz (LL) equation, which describes the irreversible and deterministic dynamics of magnetic moments. The resulting stochastic Landau-Lifshitz (sLL) equation obeys detailed balance, which guarantees that, with the external field fixed, the system converges to thermodynamic equilibrium with vanishing entropy production and with non-vanishing probability current. We then discuss various thermodynamic variables both at the trajectory level and at the ensemble level, and further establish both the first and the second laws of thermodynamics. Finally, we establish fluctuation theorems, and verify them using numerical simulations.