Abstract A Markov process can be invariant under time reversal and it also can exhibit a failure of invariance that is “uniformly positive.” I show how each of these possibilities contributes to the project of deciding when a temporal sequence of states has a higher probability than its mirror image. Neither suffices, but a distinct property of the Markov process completes the project, namely the unconditional probabilities of two possible states of the system at the start of the process. The concept of forward time-translational invariance plays a role in the analysis, but I discuss backward time-translational invariance as well. I argue that the Markov framework helps clarify how the Past Hypothesis (the hypothesis that the universe began in a very low entropy state) is related to the Second Law of Thermodynamics, and how each is relevant to explaining why histories that exhibit entropy increase have higher probabilities than histories that exhibit entropy decline. I argue that the Past Hypothesis, if true, helps explain this fact about histories, but a far weaker hypothesis about the universe's initial state suffices to do so.

中文翻译：

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历史，动力学定律和初始条件-时间可逆性不变性及其在马尔可夫过程中的失败，并应用于热力学第二定律和过去的假设

摘要马尔可夫过程在时间反转下可以不变，也可以表现出“一致正”的不变性失败。我展示了这些可能性中的每一种如何有助于确定状态的时间序列何时具有比其镜像更高的概率的项目。这两个条件都不足够，但马尔可夫过程的独特属性使项目得以完成，即过程开始时系统的两种可能状态的无条件概率。正向时间平移不变性的概念在分析中起作用，但我也讨论了反向时间平移不变性。我认为，马尔可夫框架有助于阐明过去假说（宇宙从非常低的熵状态开始的假说）与热力学第二定律的关系，以及与解释熵增加的历史为什么比显示熵减少的历史具有更高概率的原因相关。我认为过去假说（如果成立）可以帮助解释有关历史的事实，但是关于宇宙初始状态的假设要弱得多，足以做到这一点。