时间之箭中的决策
Decision Making in the Arrow of Time
摘要：
我们证明了随机过程的稳态熵产生率与决定时间箭头方向所需的最小时间成反比。在这里，我们应用Wald的序贯概率比检验，以最佳地决定在平稳马尔可夫过程的时间箭头的方向。此外，稳态熵产生率可以估计使用合适的物理变量的平均首次通过时间。我们推导出一个首达时间波动定理，这意味着正确和错误的决策时间分布是相等的。我们的结果说明了两个简单的例子的非平衡过程的数值模拟。
英文摘要：
We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald's sequential probability ratio test to optimally decide on the direction of time's arrow in stationary Markov processes. Furthermore the steady state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes.
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