An Identity of Chernoff Bounds With an Interpretation in Statistical Physics and Applications in Information Theory

An identity between two versions of the rate function of the probability a certain large deviations event is established. This identity has an interpretation in statistical physics, namely, an isothermal equilibrium of a composite system that consists of multiple subsystems of particles. Several information-theoretic application examples, where the analysis of this large deviations probability naturally arises, are then described from the viewpoint of this statistical mechanical interpretation. This results in several relationships between information theory and statistical physics, which we hope, the reader will find insightful.