Continuous information flow fluctuations

Information plays a pivotal role in the thermodynamics of nonequilibrium processes with feedback. However, much remains to be learned about the nature of information fluctuations in small-scale devices and their relation with fluctuations in other thermodynamics quantities, like heat and work. Here we derive a series of fluctuation theorems for information flow and partial entropy production in a Brownian particle model of feedback cooling and extend them to arbitrary driven diffusion processes. We then analyze the long-time behavior of the feedback-cooling model in detail. Our results provide insights into the structure and origin of large deviations of information and thermodynamic quantities in autonomous Maxwell's demons.