The large deviation function for entropy production: the optimal trajectory and the role of fluctuations
The large deviation function for entropy production: the optimal trajectory and the role of fluctuations
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熵产生的大偏差函数：最优轨迹和波动的作用
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发表时间：
2012
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通讯作者：
U. Seifert
中科院分区：
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作者：
T. Speck;A. Engel;U. Seifert
研究了离散格子上的非对称随机游动和连续周期势中的布朗运动两个一维驱动系统的大偏差函数的熵产生率。我们比较了两种方法：使用Donsker-Varadhan理论和使用Freidlin-Wentzell理论。我们证明了大偏差函数的两翼由单一的最优轨迹支配：要么正向(正率)，要么反向(负率)。这两个分支在零熵产生时的连接意味着不可微性，因此出现了“扭结”。然而，在零熵产生附近，许多轨迹起到了作用，因此“扭结”被抹掉了。
We study the large deviation function for the entropy production rate in two driven one-dimensional systems: the asymmetric random walk on a discrete lattice and Brownian motion in a continuous periodic potential. We compare two approaches: using the Donsker–Varadhan theory and using the Freidlin–Wentzell theory. We show that the wings of the large deviation function are dominated by a single optimal trajectory: either in the forward direction (positive rate) or in the backward direction (negative rate). The joining of the two branches at zero entropy production implies a non-differentiability and thus the appearance of a ‘kink’. However, around zero entropy production, many trajectories contribute and thus the ‘kink’ is smeared out.