标题： 随机动力学中的涨落谱和粗粒化 显示英文标题

标题： Fluctuation Spectra and Coarse Graining in Stochastic Dynamics

摘要： 小生物系统中的涨落可能对其功能至关重要。 大偏差理论从随机过程的角度表征这些罕见事件。 在大多数情况下，直接确定大偏差函数是非常困难的。 为了避免这种必要性，我提出一种方法，用于量化具有有限状态空间的任意马尔可夫模型的涨落谱。 在非平衡条件下，类似电流的可观测量特别值得关注。 所有类似电流的可观测量的空间具有自然分解为正交补集。 值得注意的是，任何可观测量的涨落谱完全由这些分量中的一个决定。 该方法被应用于研究在不同分辨率下采样相同动力学的设置中的涨落差异。 粗粒化将这些模型联系起来，并且可以以保持可观测量期望值的方式进行。 然而，粗粒化对涨落的影响并不明显。 这些差异在简单的模型系统中被明确地推导出来。 显示英文摘要

摘要： Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the large-deviation functions. Circumventing this necessity, I present a method to quantify the fluctuation spectra for arbitrary Markovian models with finite state space. Under non-equilibrium conditions, current-like observables are of special interest. The space of all current-like observables has a natural decomposition into orthogonal complements. Remarkably, the fluctuation spectrum of any observable is entirely determined by only one of these components. The method is applied to study differences of fluctuations in setups sampling the same dynamics at different resolutions. Coarse graining relates these models and can be done in a way that preserves expectation values of observables. However, the effects of the coarse graining on the fluctuations are not obvious. These differences are explicitly worked out for a simple model system.