Relations Between Tsallis and Kaniadakis Entropic Measures and Rigorous Discussion of Conditional Kaniadakis Entropy

Author(s): Amelia Carolina Sparavigna

Tsallis and Kaniadakis entropies are generalizing the Shannon entropy and have it as their limit when their entropic indices approach specific values. Here we show some relations existing between Tsallis and Kaniadakis entropies. We will also propose a rigorous discussion of the conditional Kaniadakis entropy, deduced from these relations.

Entropy, Generalized Entropies

1. Shannon, C.E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal 2 (3):379–423. DOI: 10.1002/j.1538-7305.1948.tb01338.x
2. Borda, M. (2011). Fundamentals in Information Theory and Coding. Springer. ISBN 978-3-642-20346-6.
3. Tsallis, C. (1960). Possible Generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics, 1988, 52: 479–487. DOI:10.1007/BF01016429
4. Kaniadakis, G.(2002). Statistical Mechanics in the Context of Special Relativity, Phys. Rev. E, 2002, 66, 056125. DOI: 10.1103/physreve.66.056125
5. Sparavigna, A.C. (2015). On the Generalized Additivity of Kaniadakis Entropy, Int. J. Sci. 4(2):44-48. DOI: 10.18483/ijSci.627
6. Kaniadakis, G. (2001). Non-linear kinetics underlying generalized statistics, Physica A 296(3-4):405-425. DOI: 10.1016/s0378-4371(01)00184-4
7. Santos, P.; Silva R.; Alcaniz J.S.; Anselmo, D.H.A.L. (2011). Generalized quantum entropies Physics Letters A 375:3119–3123. DOI: 10.1016/j.physleta.2011.07.001
8. Scarfone, A.M.; Wada, T. Thermodynamic equilibrium and its stability for microcanonical systems described by the Sharma-Taneja-Mittal entropy, 2005, Phys. Rev. E 72, 026123. DOI: 10.1103/physreve.72.026123
9. Sparavigna, A.C. (2015). Mutual Information and Nonadditive Entropies: A Method for Kaniadakis Entropy, International Journal of Sciences 10(2015):5-8. DOI: 10.18483/ijSci.846
10. Abe, S.; Rajagopal, A.K. (2000). Nonadditive Conditional Entropy and its Significance for Local Realism, arXiv:quant-ph/0001085, 24 Jan 2000.