A Fractional Entropy in Fractal Phase Space: Properties and Characterization. (23rd September 2014)

• Record Type: Journal Article
• Authors: Radhakrishnan, Chandrashekar; Chinnarasu, Ravikumar; Jambulingam, Segar
• Other Names: Pennini Flavia Academic Editor.
• Is Part Of: International journal of statistical mechanics. Volume 2014(2014)
• Publication Date: 2014-09-23
• Subjects: Statistical mechanics -- Periodicals; Statistical mechanics; Periodicals; 530.13
• DOI: 10.1155/2014/460364
• Languages: English
• ISSNs: 2356-7112

Abstract

Abstract : A two-parameter generalization of Boltzmann-Gibbs-Shannon entropy based on natural logarithm is introduced. The generalization of the Shannon-Khinchin 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, the relative Fisher information, and the Jensen-Fisher information corresponding to this entropy are also derived. Also the Lesche stability and the thermodynamic stability conditions are verified. We propose a generalization of a complexity measure and apply it to a two-level system and a system obeying exponential distribution. Using different distance measures we define the statistical complexity and analyze it for two-level and five-level system.