Relaxation-speed crossover in anharmonic potentials

TL;DR

This paper investigates how overdamped diffusion in anharmonic potentials can exhibit both faster heating and cooling, revealing a phase diagram with regions of different relaxation speed behaviors and a crossover zone.

Contribution

It introduces a relaxation-speed phase diagram for anharmonic potentials, identifying conditions for faster heating, cooling, and a crossover behavior, extending previous findings.

Findings

Overdamped diffusion shows both faster heating and cooling depending on parameters.

A phase diagram maps different relaxation speed regimes in anharmonic potentials.

A crossover region exists where heating transitions from slower to faster asymptotically.

Abstract

In a recent Letter [A. Lapolla and A. Godec, Phys. Rev. Lett. 125, 110602 (2020)], thermal relaxation was observed to occur faster from cold to hot (heating) than from hot to cold (cooling). Here we show that overdamped diffusion in anharmonic potentials generically exhibits both faster heating and faster cooling, depending on the initial temperatures and on the potential's degree of anharmonicity. We draw a relaxation-speed phase diagram that localises the different behaviours in parameter space. In addition to faster-heating and faster-cooling regions, we identify a crossover region in the phase diagram, where heating is initially slower but asymptotically faster than cooling. The structure of the phase diagram is robust against the inclusion of a confining, harmonic term in the potential as well as moderate changes of the measure used to define initially equidistant temperatures.