Asymmetric thermal relaxation in driven systems: Rotations go opposite ways

Abstract

It was predicted and recently experimentally confirmed that systems with microscopically reversible dynamics in quadratic potentials warm up faster than they cool down. This thermal relaxation asymmetry challenged our understanding of relaxation far from equilibrium. Because the intuition and proof hinged on the dynamics obeying detailed balance, it was not clear whether the asymmetry persists in systems with irreversible dynamics. To fill this gap, we here prove the relaxation asymmetry for systems driven out of equilibrium by a general linear drift. The asymmetry persists due to a nontrivial isomorphism between driven and reversible processes. Moreover, rotations of level sets of probability densities emerge that, strikingly, occur in opposite directions during heating and cooling. This highlights that noisy systems do not relax by passing through local equilibria.