Asymptotic analysis for the Generalized Relativistic Langevin Equation

Ethan Baker; Manh Hong Duong; Hung Dang Nguyen

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arXiv · 2603.15088

Asymptotic analysis for the Generalized Relativistic Langevin Equation

Ethan Baker·Manh Hong Duong·Hung Dang Nguyen

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Abstract

In this paper, we study a non-Markovian generalized relativistic Langevin equation (GRLE). We show that when the memory kernel is a sum of exponentials, the GRLE is equivalent to a Markovian system with added variables. We establish the well-posedness and polynomial ergodicity, obtaining an algebraic rate of convergence to the unique Gibbs distribution. From the Markovian GRLE, we recover the relativistic underdamped Langevin dynamics in a small-noise limit, as well as the classical (non-relativistic) generalized Langevin dynamics in the Newtonian limit.

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Ethan Baker, Manh Hong Duong, Hung Dang Nguyen. 2026-03-16. Asymptotic analysis for the Generalized Relativistic Langevin Equation. https://arxiv.org/abs/2603.15088

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