Institute of Problems of Chemical Physics, Academy of Sciences of Russia, Chernogolovka, Moscow Region, 142432 Russia.
Phys Rev E. 2018 Feb;97(2-1):022122. doi: 10.1103/PhysRevE.97.022122.
Some analogies between different nonequilibrium heat conduction models, particularly random walk, the discrete variable model, and the Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that, under an assumption of a finite value of the heat carrier velocity, these models lead to the hyperbolic heat conduction equation and the modified Fourier law with relaxation term. Corresponding effective temperature and entropy have been introduced and analyzed. It has been demonstrated that the effective temperature, defined as a geometric mean of the kinetic temperatures of the heat carriers moving in opposite directions, acts as a criterion for thermalization and is a nonlinear function of the kinetic temperature and heat flux. It is shown that, under highly nonequilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature, heat capacity, and local entropy go to zero even at a nonzero equilibrium temperature. This provides a possible generalization of the third law to nonequilibrium situations. Analogies and differences between the proposed effective temperature and some other definitions of a temperature in nonequilibrium state, particularly for active systems, disordered semiconductors under electric field, and adiabatic gas flow, have been shown and discussed. Illustrative examples of the behavior of the effective temperature and entropy during nonequilibrium heat conduction in a monatomic gas and a strong shockwave have been analyzed.
已经讨论了不同非平衡热传导模型之间的一些类比，特别是随机漫步、离散变量模型和具有单松弛时间近似的玻尔兹曼输运方程。我们表明，在热载体速度有限值的假设下，这些模型导致双曲热传导方程和具有松弛项的修正傅立叶定律。引入并分析了相应的有效温度和熵。已经证明，有效温度定义为沿相反方向运动的热载体的动温度的几何平均值，作为热化的判据，并且是动温度和热通量的非线性函数。已经表明，在高度非平衡条件下，当热通量趋于其可能的最大值时，即使在非零平衡温度下，有效温度、热容和局部熵也会趋于零。这为非平衡情况下的第三定律提供了一种可能的推广。已经展示和讨论了所提出的有效温度与非平衡态中其他一些温度定义之间的相似性和差异，特别是对于主动系统、电场下的无序半导体和绝热气流。分析了单原子气体和强冲击波中非平衡热传导期间有效温度和熵的行为的实例。
