Large deviations and fluctuation theorems for cycle currents defined in the loop-erased and spanning tree manners: a comparative study

Yuhao Jiang, Bingjie Wu, Chen Jia

Published 2022-04-05Version 1

The cycle current is a crucial quantity in stochastic thermodynamics. The absolute and net cycle currents of a Markovian system can be defined in the loop-erased (LE) or the spanning tree (ST) manner. Here we make a comparative study between the large deviations and fluctuation theorems for the LE and ST currents, i.e. cycle currents defined in the LE and ST manners. First, we derive the exact joint distribution and the large deviation rate function for the LE currents of a system with a cyclic topology and also obtain the rate function for the ST currents of a general system. The relationship between the rate functions for the LE and ST currents is clarified. Furthermore, we examine various types of fluctuation theorems satisfied by the LE and ST currents and clarify their ranges of applicability. We show that both the absolute and net LE currents satisfy the strong form of all types of fluctuation theorems. In contrast, the absolute ST currents do not satisfy fluctuation theorems, while the net ST currents only satisfy the weak form of fluctuation theorems under the periodic boundary condition.