We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature gradients imposed by reservoirs at the ends of the channel. In our model, walkers interact with other walkers at the same site by sharing energy at each time step, but the amount of energy carried does not affect the motion of the walkers. We find that already in this simple model long-range correlations arise in the nonequilibrium stationary state which are similar to those observed in more realistic models of coupled transport.
Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part III Extensions and applications to kinetic theory and transport
Heat transport in stochastic energy exchange models of locally confined hard spheres
我们研究了一类随机能量交换系统中的热输运，该系统的特征是在相邻粒子进行罕见的二元碰撞的假设下，局部捕获的硬球网络的相互作用。我们的结果提供了对先前应用于受限二维硬盘的动态的三维动态的扩展[Gaspard P & Gilbert T On the derivation of Fourier's law in stochastic energy exchange systems J Stat Mech（2008）P11021]。值得注意的是，导热率在这里又由能量交换的频率给出。此外，在这种情况下，指定能量交换动力学的随机核的表达更简单，因此允许更快和更广泛的数值计算。
