Large deviations and deterministic measures of information

In recent years, Large Deviations theory has found important applications in many areas of engineering and science including communication and control systems. The objective of this note is to introduce and explore connections between certain fundamental concepts of Large Deviations theory and Information Theory, by introducing deterministic measures of information. The connections are established through the so-called rate functional associated with the Large Deviations principle, which lead to a natural definition of (max, plus) deterministic measure of information.