A Fractional entropy in Fractal phase space: properties and characterization

R. Chandrashekar; C. Ravikumar; J. Segar

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arXiv · 1301.2779

A Fractional entropy in Fractal phase space: properties and characterization

R. Chandrashekar·C. Ravikumar·J. Segar

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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.

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R. Chandrashekar, C. Ravikumar, J. Segar. 2013-03-07. A Fractional entropy in Fractal phase space: properties and characterization. https://arxiv.org/abs/1301.2779

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