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 localizes the different behaviors 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.

中文翻译：

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非谐势中的弛豫速度交叉

在最近的一封信中 [A. Lapolla 和 A. Godec，物理学。牧师莱特。 125, 110602 (2020)]，观察到从冷到热（加热）的热弛豫比从热到冷（冷却）发生得更快。在这里，我们表明非谐势中的过阻尼扩散通常表现出更快的加热和更快的冷却，这取决于初始温度和势的非谐程度。我们绘制了一个弛豫速度相图，用于定位参数空间中的不同行为。除了快速加热和快速冷却区域之外，我们还在相图中确定了一个交叉区域，其中加热最初较慢但渐近地比冷却快。相图的结构对于在电势中包含限制性谐波项以及用于定义初始等距温度的度量的适度变化是稳健的。