Markov models are widely used to describe stochastic dynamics. Here, we show that Markov models follow directly from the dynamical principle of maximum caliber (Max Cal). Max Cal is a method of deriving dynamical models based on maximizing the path entropy subject to dynamical constraints. We give three different cases. First, we show that if constraints (or data) are given in the form of singlet statistics (average occupation probabilities), then maximizing the caliber predicts a time-independent process that is modeled by identical, independently distributed random variables. Second, we show that if constraints are given in the form of sequential pairwise statistics, then maximizing the caliber dictates that the kinetic process will be Markovian with a uniform initial distribution. Third, if the initial distribution is known and is not uniform we show that the only process that maximizes the path entropy is still the Markov process. We give an example of how Max Cal can be used to discriminate between different dynamical models given data.
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机译：马尔可夫模型被广泛用于描述随机动力学。在这里，我们表明马尔可夫模型直接遵循最大口径（Max Cal）的动力学原理。 Max Cal是一种基于最大化受动态约束的路径熵来导出动力学模型的方法。我们给出三种不同的情况。首先，我们表明，如果以单重态统计（平均职业概率）的形式给出约束（或数据），则最大化口径可预测一个由时间独立的过程，该过程由相同的，独立分布的随机变量建模。其次，我们表明，如果以顺序成对统计的形式给出约束，则最大化口径将指示动力学过程将是具有统一初始分布的马尔可夫模型。第三，如果初始分布是已知的并且不是均匀的，我们表明使路径熵最大化的唯一过程仍然是马尔可夫过程。我们给出一个示例，说明如何使用Max Cal区分给定数据的不同动力学模型。
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