Ford Ian J, Laker Zachary P L, Charlesworth Henry J
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042108. doi: 10.1103/PhysRevE.92.042108. Epub 2015 Oct 5.
We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the one-dimensional stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the Kramers equation to determine the behavior of an ensemble of systems. We express the total stochastic entropy production in terms of a relaxational or nonadiabatic part together with two components of housekeeping entropy production and determine the distributions for each, demonstrating the importance of all three contributions for this system. We compare the results with an approximate analytic model of the mean behavior and we further demonstrate that the total entropy production and the relaxational component approximately satisfy detailed fluctuation relations for certain time intervals. Finally, we comment on the resemblance between the procedure for solving the Kramers equation and a constrained extremization, with respect to the probability density function, of the spatial density of the mean rate of production of stochastic entropy.
我们计算了与通过耦合到随时间变化的非等温热浴的系统进行的非平稳热传输相关的随机熵产生的统计特性。我们通过数值求解适当的朗之万方程，并使用克莱默斯方程的近似解析解来确定系统系综的行为，研究了在这种环境中束缚粒子的一维随机演化。我们用弛豫或非绝热部分以及两个家务熵产生分量来表示总随机熵产生，并确定每个分量的分布，证明了这三个贡献对该系统的重要性。我们将结果与平均行为的近似解析模型进行比较，并进一步证明总熵产生和弛豫分量在特定时间间隔内近似满足详细涨落关系。最后，我们评论了求解克莱默斯方程的过程与关于随机熵产生平均速率的空间密度的概率密度函数的约束极值化之间的相似性。
