On axiomatization of conditional entropy of functions between finite sets

In this paper we present a new axiomatization of the notion of entropy of functions between finite sets and we introduce and axiomatize the notion of conditional entropy between functions. The results can be directly applied to logic functions, which can be regarded as functions between finite sets. Our axiomatizations are based on properties of entropy with regard to operations commonly applied to discrete functions and are related to the usage of entropy as a measure of the energy dissipated by circuits that implement discrete functions.