An Informational Proof of H-Theorem

Abstract

After a historical reconstruction of the main Boltzmann’s ideas on mechanical statistics, a discrete version of Boltzmann’s H-theorem is proved, by using basic concepts of information theory. Namely, H-theorem follows from the central limit theorem, acting inside a closed physical system, and from the maximum entropy law for normal probability distributions, which is a consequence of Kullback-Leibler entropic divergence positivity. Finally, the relevance of discreteness and probability, for a deep comprehension of the relationship between physical and informational entropy, is analyzed and discussed in the light of new perspectives emerging in computational genomics.