非线性阻力下分子气体中的Mpemba效应
Mpemba effect in molecular gases under nonlinear drag
摘要：
我们研究Mpemba效应-具体地，气体粒子通过弹性碰撞在它们之间相互作用，并且还与处于平衡的背景流体相互作用。因此，在动力学理论的框架内，我们的气体由Enskog-Fokker-Planck方程描述。在第一Sonine近似下进行分析，其中温度的演变与过量峰度的演变相耦合。这种耦合导致出现的Mpemba效应，这是观察到的早期阶段的松弛，当两个样品的初始温度足够接近。这使得一个简单的理论，线性化的温度演变周围的参考温度-即初始温度接近渐近平衡值的发展。线性理论提供了一个半定量的描述的效果，包括交叉时间和最大温差的表达式。我们还讨论了我们的线性化理论的局限性。
英文摘要：
We look into the Mpemba effect---the initially hotter sample cools sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and also with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog--Fokker--Planck equation. The analysis is carried out in the first Sonine approximation, in which the evolution of the temperature is coupled to that of the excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed in an early stage of the relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature---namely the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for the crossover time and the maximum temperature difference. We also discuss the limitations of our linearized theory.
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