从最大口径原理看统计力学中的预测与反演
Prediction and Retrodiction in Statistical Mechanics from the Principle of Maximum Caliber
摘要：
一个统计的，路径依赖的框架来描述时间依赖的宏观理论，使用最大口径的原则。通过这个过程，它是可能的推断预测非平衡统计力学模型从变分原理，提供了足够的时间相关的约束条件和系统在某些特定的时间的状态。该方法的例子是通过获得一个依赖于时间的布朗粒子的动力学限制的描述。我们将模型的预测性质与先验分布的结构联系起来，先验分布代表了在考虑动态约束之前系统的知识状态。非预测模型被证明是可能的，在所提出的框架和作为一个例子，追溯动力学从相同的动力学约束。
英文摘要：
A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical mechanical models from a variational principle, provided that the adequate time-dependent constraints and the state of the system at some specific times are given. The approach is exemplified by obtaining the description of a time-dependent Brownian particle from kinetic restrictions. We relate the predictive nature of a model to the structure of the prior distribution that represents the state of knowledge about the system before the dynamical constraints are considered. Non-predictive models are shown to be possible in the presented framework and as an example, retrodictive dynamics are obtained from the same kinetic constraints.
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