Lesche Stability of $\kappa$-Entropy

Abstract

The Lesche stability condition for the Shannon entropy [B. Lesche, J. Stat. Phys. 27, 419 (1982)], represents a fundamental test, for its experimental robustness, for systems obeying the Maxwell-Boltzmann statistical mechanics. Of course, this stability condition must be satisfied by any entropic functional candidate to generate non-conventional statistical mechanics. In the present effort we show that the $\kappa$-entropy, recently introduced in literature [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002)], satisfies the Lesche stability condition.

Presented at next2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy, 21st-28th September 2003. In press Physica A (2004). Elsevier LaTeX macros, 10 pages, minor changes

References in corpus (5)

• Statistical mechanics in the context of special relativity
• Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions
• Nonextensive statistical mechanics: A brief introduction
• Generalized entropy optimized by an arbitrary distribution
• Continuity of a class of entropies and relative entropies

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