论文标题
功能统计物理学：Feynman - KAC公式和信息几何形状
Functorial Statistical Physics: Feynman--Kac Formulae and Information Geometries
论文作者
论文摘要
本文的主要结果包括以下两个相关事实的证明：（i）Feynman--KAC公式是函数$ f _*$，即，在统计歧管上的随机微分方程和动力学系统之间，（ii）统计分歧是该函数在灯尺胶合胶的条件下产生的统计分歧。然后，将特定的局部属性用于$ f _*$，从函数量子场理论识别为“缝制定律”，然后将结果扩展到Chapman-Kolmogorov方程{\ IT}最大熵原理的时间依赖性概括。这产生了一条分别形式化的变异原则，这使我们超越了Feynman-KAC衡量了Wiener Laws驱动的。我们的构建对更深层次的理论提供了强烈的瞥见，我们认为重新想象时间依赖时间的统计物理和信息几何形状。
The main results of this paper comprise proofs of the following two related facts: (i) the Feynman--Kac formula is a functor $F_*$, namely, between a stochastic differential equation and a dynamical system on a statistical manifold, and (ii) a statistical manifold is a sheaf generated by this functor with a canonical gluing condition. Using a particular locality property for $F_*$, recognised from functorial quantum field theory as a `sewing law,' we then extend our results to the Chapman--Kolmogorov equation {\it via} a time-dependent generalisation of the principle of maximum entropy. This yields a partial formalisation of a variational principle which takes us beyond Feynman--Kac measures driven by Wiener laws. Our construction offers a robust glimpse at a deeper theory which we argue re-imagines time-dependent statistical physics and information geometry alike.
