Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined by the q−logarithm and the q−exponential functions to the definition of the likelihood function in Gauss' law of… (More)
The Shannon-Khinchin axioms are generalized to nonextensive systems and the uniqueness theorem for the nonextensive entropy is proved rigorously. In the present axioms, Shannon additivity is used as additivity in contrast to pseudoadditivity in Abe's axioms. The results reveal that Tsallis entropy is the simplest among all nonextensive entropies which can… (More)
Based on the κ-deformed functions (κ-exponential and κ-logarithm) and associated multiplication operation (κ-product) introduced by Kaniadakis (Phys. Rev. E 66 (2002) 056125), we present another one-parameter generalization of Gauss' law of error. The likelihood function in Gauss' law of error is generalized by means of the κ-product. This κ-generalized… (More)
The quantum mutual entropy was introduced by one of the present authors in 1983 as a quantum extension of the Shannon mutual information. It has been used for several studies such as quantum information transmission in optical communication and quantum irreversible processes. In this paper, a nonlinear channel for a quantum teleportation process is… (More)
—The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise q-Stirling's formula. The α-divergence (or q-divergence) is uniquely derived from the generalized binomial distribution in the sense that when α → −1 (i.e., q → 1) it recovers KL divergence obtained from the standard binomial… (More)
Stirling approximation of the factorials and multinominal coefficients are generalized based on the one-parameter (κ) deformed functions introduced by Kaniadakis [Phys. Rev. E 66 (2002) 056125]. We have obtained the relation between the κ-generalized multinominal coefficients and the κ-entropy by introducing a new κ-product operation.