论文标题
在基于循环和跨越树木的循环电流的大偏差和波动定理：比较研究
Large deviations and fluctuation theorems for cycle currents defined in the loop-erased and spanning tree manners: a comparative study
论文作者
论文摘要
循环电流是随机热力学的关键量。马尔可夫系统的绝对和净循环电流可以在基于环的（LE）或跨越树（ST）方式中定义。在这里，我们在LE和ST电流的大偏差和波动定理之间进行了比较研究，即在LE和ST举止中定义的循环电流。首先，我们得出具有循环拓扑的系统的LE电流的确切关节分布和较大的偏差率函数，并获得了通用系统的ST电流的确切速率函数。阐明了LE和ST电流的速率函数之间的关系，并应用分析结果以检查三步可逆酶反应的产品速率的波动。此外，我们研究了LE和ST电流满足的各种类型的波动定理，并阐明了它们的适用性范围。我们表明，绝对和净电流都满足所有类型的波动定理的强大形式。相比之下，绝对ST电流不满足波动定理，而净ST电流仅满足周期性边界条件下波动定理的弱形式。
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 spanning tree (ST) manner. Here we make a comparative study between the large deviations and fluctuation theorems for LE and ST currents, i.e. cycle currents defined in the LE and ST manners. First, we derive the exact joint distribution and large deviation rate function for the LE currents of a system with a cyclic topology and also obtain the exact rate function for the ST currents of a general system. The relationship between the rate functions for LE and ST currents is clarified and the analytical results are applied to examine the fluctuations in the product rate of a three-step reversible enzyme reaction. Furthermore, we examine various types of fluctuation theorems satisfied by 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.
