Quantifying non-Markovianity in magnetization dynamics via entropy production rates

Abstract Magnetization dynamics is commonly described by the stochastic Landau-Lifshitz-Gilbert (LLG) equation. However, on picosecond timescales, inertial and open-system extensions of the LLG equation are necessary to interpret recent experiments. While it has been anticipated that these extensions make the magnetization dynamics non-Markovian, to date, the question of the extent of non-Markovianity has remained unanswered. Here, we provide a systematic quantification of the degree of non-Markovianity in these magnetization models using established measures. We find that, while the standard LLG equation exhibits strictly positive entropy production rates, inertial and open-system LLG dynamics display temporarily negative entropy production rates, which signal non-Markovian dynamics, as we demonstrate both analytically and numerically. Our numerical calculations show that experiments requiring the open-system LLG equation are more non-Markovian than those described by classical or inertial LLG equations.