Table of Contents
International Journal of Statistical Mechanics
Volume 2014, Article ID 460364, 16 pages
Research Article

A Fractional Entropy in Fractal Phase Space: Properties and Characterization

1The Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600 113, India
2Department of Physics, National Chung Hsing University, 250 Kuo Kuang Road, Taichung 40227, Taiwan
3Department of Theoretical Physics, University of Madras, Maraimalai Campus, Guindy, Chennai 600 025, India
4Department of Physics, National Tsing Hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan
5Ramakrishna Mission Vivekananda College, Mylapore, Chennai 600 004, India

Received 27 May 2014; Accepted 24 August 2014; Published 24 September 2014

Academic Editor: Flavia Pennini

Copyright © 2014 Chandrashekar Radhakrishnan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.