II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany.
Department of Physics, University of Seoul, 02504 Seoul, Korea.
Phys Rev E. 2019 Jan;99(1-1):012136. doi: 10.1103/PhysRevE.99.012136.
The entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative. The housekeeping entropy production, which is a part of total entropy production, is associated with the heat dissipation in maintaining a nonequilibrium steady state. We derive a Langevin-type stochastic differential equation for the housekeeping entropy production. The equation allows us to define a housekeeping entropic time τ. Remarkably it turns out that the probability distribution of the housekeeping entropy production at a fixed value of τ is given by the Gaussian distribution regardless of system details. The Gaussian distribution is universal for any systems, whether in the steady state or in the transient state and whether they are driven by time-independent or time-dependent driving forces. We demonstrate the universal distribution numerically for model systems.
非平衡系统中打破详细平衡的熵产生是一个随机变量，其平均值是非负的。维持非平衡稳态所涉及的维持熵产生是总熵产生的一部分。我们推导出了一个关于维持熵产生的朗之万型随机微分方程。该方程允许我们定义一个维持熵产生的时间 τ。值得注意的是，事实证明，无论系统细节如何，在固定 τ 值下维持熵产生的概率分布都是由高斯分布给出的。这种高斯分布对于任何系统都是通用的，无论是处于稳态还是瞬态，无论是由与时间无关的驱动力还是与时间相关的驱动力驱动。我们通过对模型系统进行数值模拟证明了这种通用分布的存在。
