Morriss Gary P, Truant Daniel P
School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):062144. doi: 10.1103/PhysRevE.87.062144. Epub 2013 Jun 28.
We explore the consequences of a deterministic microscopic thermostat-reservoir contact mechanism. With different temperature reservoirs at each end of a two-dimensional system, a heat current is produced and the system has an anomalous thermal conductivity. The microscopic form for the local heat flux vector is derived and both the kinetic and potential contributions are calculated. The total heat flux vector is shown to satisfy the continuity equation. The properties of this nonequilibrium steady state are studied as functions of system size and temperature gradient, identifying key scaling relations for the local fluid properties and separating bulk and boundary effects. The local entropy density calculated from the local equilibrium distribution is shown to be a very good approximation to the entropy density calculated directly from the velocity distribution even for systems that are far from equilibrium. The dissipation and kinetic entropy production and flux are compared quantitatively and the differing mechanisms discussed within the Bhatnagar-Gross-Krook approximation. For equal-temperature reservoirs the entropy production near the reservoir walls is shown to be proportional to the local phase space contraction calculated from the tangent space dynamics. However, for unequal temperatures, the connection between local entropy production and local phase space contraction is more complicated.
我们探究了一种确定性微观恒温器 - 储热器接触机制的后果。在二维系统的两端设置不同温度的储热器，会产生热流，且系统具有反常热导率。我们推导了局部热流矢量的微观形式，并计算了动力学贡献和势能贡献。结果表明总热流矢量满足连续性方程。研究了这种非平衡稳态的性质与系统尺寸和温度梯度的函数关系，确定了局部流体性质的关键标度关系，并区分了体效应和边界效应。即使对于远离平衡的系统，由局部平衡分布计算得到的局部熵密度也被证明是直接从速度分布计算得到的熵密度的一个非常好的近似。在Bhatnagar - Gross - Krook近似下，对耗散、动力学熵产生和通量进行了定量比较，并讨论了不同的机制。对于等温储热器，储热器壁附近的熵产生与根据切空间动力学计算得到的局部相空间收缩成正比。然而，对于不等温情况，局部熵产生与局部相空间收缩之间的联系更为复杂。
