Brownian motion with stochastic energy renewals

TL;DR

This paper studies how intermittent energy injections affect Brownian particles, revealing non-Boltzmannian energy distributions, non-monotonic diffusion, and deviations from equilibrium, with implications for understanding non-equilibrium thermodynamics.

Contribution

It introduces a model of Brownian motion with stochastic energy renewals, analyzing non-equilibrium energy distributions and response relations, extending to non-Poissonian processes.

Findings

Energy distributions are non-Boltzmannian with a shape transition.

Effective diffusion coefficient shows non-monotonic behavior.

Modified fluctuation-response relation indicates absence of a consistent effective temperature.

Abstract

We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For energy renewals occurring at a constant rate, we find non-Boltzmannian energy distributions that undergo a shape transition driven by the competition between the velocity relaxation timescale and the renewal timescale. In the limit of rapid renewals, the dynamics mimics one-dimensional run-and-tumble motion, while at finite renewal rates, the effective diffusion coefficient exhibits non-monotonic behavior. To quantify the system's departure from equilibrium, we derive a modified fluctuation-response relation and demonstrate the absence of a consistent effective temperature. The dissipation is characterized by deviations from equilibrium-like response, captured via the Harada-Sasa relation. Finally, we extend the analysis to non-Poissonian renewal processes and introduce a dimensionless conversion coefficient that quantifies the thermodynamic cost of diffusion.