$\alpha$-divergence derived as the generalized rate function in a power-law system

Abstract

The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise $q$-Stirling's formula. The $\alpha$-divergence (or $q$-divergence) is uniquely derived from the generalized binomial distribution in the sense that when $\alpha \to -1$ (i.e., $q\to 1$) it recovers KL divergence obtained from the standard binomial distribution. Based on these combinatorial considerations, it is shown that $\alpha$-divergence (or $q$-divergence) is appeared as the generalized rate function in the large deviation estimate in Tsallis statistics.

5 pages

References in corpus (5)

• The large deviation approach to statistical mechanics
• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Generalized algebra within a nonextensive statistics
• Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized $q$-average energy
• Entropic Forms and Related Algebras