Mathematical inequalities for some divergences
Abstract
Some natural phenomena are deviating from standard statistical behavior and their study has increased interest in obtaining new definitions of information measures. But the steps for deriving the best definition of the entropy of a given dynamical system remain unknown. In this paper, we introduce some parametric extended divergences combining Jeffreys divergence and Tsallis entropy defined by generalized logarithmic functions, which lead to new inequalities. In addition, we give lower bounds for one-parameter extended Fermi-Dirac and Bose-Einstein divergences. Finally, we establish some inequalities for the Tsallis entropy, the Tsallis relative entropy and some divergences by the use of the Young's inequality.
- Publication:
-
Physica A Statistical Mechanics and its Applications
- Pub Date:
- January 2012
- DOI:
- 10.1016/j.physa.2011.07.052
- arXiv:
- arXiv:1104.5603
- Bibcode:
- 2012PhyA..391..388F
- Keywords:
-
- Condensed Matter - Statistical Mechanics;
- Computer Science - Information Theory;
- Mathematics - Classical Analysis and ODEs;
- 94A17;
- 26D15
- E-Print:
- 18 pages