时间的倒钩箭：不可逆性、隐秘性和存储信息
Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
摘要：
我们展示了为什么过去和未来之间交流的信息量--过剩熵--一般来说不是现在存储的信息量--统计复杂性。这是一个长期存在的难题，因为后者是最佳预测所需的，但前者描述了观察到的行为。我们为动力系统和随机过程设计了一个分类方案，确定这两个量何时相同或不同。我们这样做是通过开发封闭形式的表达式的过剩熵的最佳因果预测和retrodictors-计算力学的ε机。一个过程的因果不可逆性和神秘性是关键的决定性属性。
英文摘要：
We show why the amount of information communicated between the past and future--the excess entropy--is not in general the amount of information stored in the present--the statistical complexity. This is a puzzle, and a long-standing one, since the latter is what is required for optimal prediction, but the former describes observed behavior. We layout a classification scheme for dynamical systems and stochastic processes that determines when these two quantities are the same or different. We do this by developing closed-form expressions for the excess entropy in terms of optimal causal predictors and retrodictors--the epsilon-machines of computational mechanics. A process's causal irreversibility and crypticity are key determining properties.
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