The uniqueness theorem for the relative entropy was proven by A.Hobson. Recently, the Tsallis entropy was characterized by H.Suyari in terms of the generalized ShannonKhinchin’s axiom. In this short paper, we characterize the Tsallis relative entropy in the finite discrete system by generalizing the conditions in Hobson’s axiom.

Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addition, some matrix trace inequalities related to the Tsallis relative entropy are studied.

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Shannon entropy of a probability measure P , defined as − ∫ X dP dμ ln dP dμ dμ on a measure space (X,M, μ), is not a natural extension from the discrete case. However, maximum entropy (ME) prescriptions of Shannon entropy functional in the measure-theoretic case are consistent with those for the discrete case. Also it is well known that Kullback-Leibler relative entropy can be extended natural...

The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...

In this paper we utilize the Tsallis relative entropy, a generalization of the Kullback–Leibler entropy in the frame work of non-extensive thermodynamics to analyze the properties of anomalous diffusion processes. Anomalous (super-) diffusive behavior can be described by fractional diffusion equations, where the second order space derivative is extended to fractional order α ∈ (1, 2). They repr...

Quantifying coherence is an essential endeavor for both quantum mechanical foundations and technologies. We present a bona fide measure of by utilizing the Tsallis relative operator (α,β)-entropy. first prove that proposed fulfills all criteria well defined measure, including strong monotonicity in resource theories coherence. then study ordering (α,β)-entropy coherence, α-entropies Rényi α-ent...

The connection between Tsallis entropy for a multifractal distribution and Jackson’s q-derivative is established. Based on this derivation and definition of a homogeneous function, a q-analogue of Shannon’s entropy is discussed. q-additivity of this entropy is shown. We also define q-analogue of Kullback relative entropy. The implications of lattice structure beneath q-calculus are highlighted ...