A Fractional entropy in Fractal phase space: properties and characterization
Abstract
A two parameter generalization of Boltzmann-Gibbs-Shannon entropy based on natural logarithm is introduced. The generalization of the Shannon-Kinchinn axioms corresponding to the two parameter entropy is proposed and verified. We present the relative entropy, Jensen-Shannon divergence measure and check their properties. The Fisher information measure, relative Fisher information and the Jensen-Fisher information corresponding to this entropy are also derived. The canonical distribution maximizing this entropy is derived and is found to be in terms of the Lambert's W function. Also the Lesche stability and the thermodynamic stability conditions are verified. Finally we propose a generalization of a complexity measure and apply it to a two level system and a system obeying exponential distribution. The results are compared with the corresponding ones obtained using a similar measure based on the Shannon entropy.
Keywords
Cite
@article{arxiv.1301.2779,
title = {A Fractional entropy in Fractal phase space: properties and characterization},
author = {R. Chandrashekar and C. Ravikumar and J. Segar},
journal= {arXiv preprint arXiv:1301.2779},
year = {2013}
}