Synchronization of two bacterial flagella as a stochastic process

Synchronization with noise is important for understanding biophysical processes at nano- and micro-meter scales, such as neuronal firing and flagellar rotations. To understand the energetics of these processes, stochastic thermodynamics approaches are useful. Due to large fluctuations in a small system, ensemble averages of thermodynamic quantities are not sufficient to characterize the energetics of an individual sample. In this paper, we use a model for synchronization of bacterial flagella as an example, and develop an approximation method for analyzing the phase and heat dissipation in trajectories for different noise realizations. We describe the {temporal evolution} of the phase difference and heat dissipation as stochastic processes, and verify the analytical results by numerical simulations.