Fluctuation Spectra and Coarse Graining in Stochastic Dynamics

Abstract: 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.