Properties of Kullback-Leibler cross-entropy minimization in nonextensive framework

Abstract

Kullback-Leibler cross-entropy has unique properties in cases involving distributions resulting from cross-entropy minimization. Nonextensive entropy (Tsallis entropy), which is a one-parameter generalization of Shannon entropy, is proposed to study certain class of physical systems. Thermostatistics based on Tsallis entropy is termed as nonextensive statistics or Tsallis statistics. Previously, Kullback-Leibler cross-entropy has been generalized and studied in this framework. In this paper we study properties of generalized cross-entropy minimization and present some differences with the classical case. In the representation of such a minimum cross-entropy distribution, we highlight the use of the q-product, an operator that has been recently introduced, to derive the mathematical structure behind the Tsallis statistics. One of our main results is the generalization of the triangle equality of cross-entropy minimization, in nonextensive framework.