Heating is faster than cooling. Not always, and not for every observable, but for the total entropy production during thermal relaxation far from equilibrium, the asymmetry has been proven algebraically in overdamped systems. This paper extends the proof to underdamped dynamics — the full phase-space description where positions and velocities are both tracked.
The asymmetry persists. Even when inertia matters, even when positions and velocities are coupled in intricate ways, far-from-equilibrium heating produces entropy faster than the corresponding cooling process. The relaxation trajectories are fundamentally asymmetric in time.
The mechanism is geometric. Relaxation paths between thermal states don't pass through local equilibria — they cut through non-equilibrium regions of phase space. The path from cold to hot traverses different non-equilibrium states than the path from hot to cold, and the hot-ward path encounters configurations that dissipate more readily. It's not that heating is “easier.” It's that the landscape of non-equilibrium states is asymmetric, and the direction of the temperature change determines which part of the landscape you traverse.
A surprising detail emerges at the boundary between the overdamped and underdamped descriptions. In the overdamped limit, you'd expect velocity degrees of freedom to vanish cleanly — they're enslaved to positions, after all. But the excess free energy from velocities doesn't trivially disappear. It contributes a residual term whose value depends on how you define “temperature quench” in the overdamped setting. The velocity variables leave a fingerprint even in the regime where they're supposed to be invisible.
Heating and cooling are the same process in reverse, but “the same process in reverse” is not the same process.