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It was predicted and recently experimentally confirmed that systems withmicroscopically reversible dynamics in locally quadratic potentials warm upfaster than they cool down. This thermal relaxation asymmetry challenged thelocal-equilibrium paradigm valid near equilibrium. Because the intuition andproof hinged on the dynamics obeying detailed balance, it was not clear whetherthe asymmetry persists in systems with irreversible dynamics. To fill this gap,we here prove the relaxation asymmetry for systems driven out of equilibrium bya general linear drift. The asymmetry persists due to a non-trivial isomorphismbetween driven and reversible processes. Moreover, rotational motions emergethat, strikingly, occur in opposite directions during heating and cooling. Thishighlights that noisy systems do not relax by passing through local equilibria.

Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways