Large deviation analysis of a simple information engine

Information thermodynamics provides a framework for studying the effect of feedback loops on entropy production. It has enabled the understanding of novel thermodynamic systems such as the information engine which can be seen as a modern version of `Maxwell's Daemon', whereby the feedback controller is acting as a Daemon, processing information gained about the system in order to do work. Here, we analyse a simple model of such an engine and provide a detailed analysis of its fluctuation properties, including the large deviations of information. We find an exact expression of the large deviation rate function for a two-site version of our model, and provide an approximate analysis for larger systems which is corroborated by simulation data.