标题： 马尔可夫通量的最佳统计：关于欧拉回路和费米子鬼粒子的故事 显示英文标题

标题： BEST statistics of Markovian fluxes: a tale of Eulerian tours and Fermionic ghosts

摘要： 我们提供了马尔可夫跳跃过程通量统计的精确表达式，在所有时间上都优于大偏差理论的渐近结果。 主要成分是枚举图论中BEST定理的一个推广，用于具有开放端点的欧拉回路。 在长时间极限下，我们重新获得了马尔可夫过程的Sanov定理，该定理通过相对熵表达了波动的指数抑制。 有限时间的幂律项随着系统大小的增加而变得越来越重要，这是一个生成树行列式，通过引入格罗斯曼变量，可以将其吸收进度量空间上与规范势耦合的费米子鬼场的有效拉格朗日量中。 参考非平衡随机热力学中的概念，度量与衡量状态之间净通信的动力学活动有关，并且与之前针对扩散过程的规范理论建立了联系。 显示英文摘要

摘要： We provide an exact expression for the statistics of the fluxes of Markov jump processes at all times, improving on asymptotic results from large deviation theory. The main ingredient is a generalization of the BEST theorem in enumeratoric graph theory to Eulerian tours with open ends. In the long-time limit we reobtain Sanov's theorem for Markov processes, which expresses the exponential suppression of fluctuations in terms of relative entropy. The finite-time power-law term, increasingly important with the system size, is a spanning-tree determinant that, by introducing Grassmann variables, can be absorbed into the effective Lagrangian of a Fermionic ghost field on a metric space, coupled to a gauge potential. With reference to concepts in nonequilibrium stochastic thermodynamics, the metric is related to the dynamical activity that measures net communication between states, and the connection is made to a previous gauge theory for diffusion processes.