Quantifying non-Markovianity in magnetization dynamics via entropy production rates

TL;DR

This paper investigates the entropy production rates in magnetization dynamics described by the LLG equation and its extensions, revealing non-Markovian behavior characterized by negative entropy production rates in inertial and open-system models.

Contribution

It analytically and numerically demonstrates the presence of non-Markovianity in extended LLG models through entropy production rates, providing a quantitative measure of non-Markovianity.

Findings

Standard LLG shows positive entropy production rates.

Inertial and open-system LLG exhibit negative entropy production rates.

Open-system LLG has the highest non-Markovianity magnitude.

Abstract

Magnetization dynamics is commonly described by the stochastic Landau-Lifshitz-Gilbert (LLG) equation. On picosecond timescales, inertial and open-system extensions of the LLG equation are necessary to interpret recent experiments. We show analytically and numerically that the standard LLG equation exhibits strictly positive entropy production rates, while inertial and open-system LLG dynamics display temporarily negative entropy production rates indicating non-Markovianity. Here we quantify the degree of non-Markovianity using established measures. Our numerical calculations show that the open-system LLG equation consistently exhibits the highest magnitude of non-Markovianity for different initial conditions and magnetic field orientations.