Related papers: Additive Entropies of degree-q and the Tsallis Ent…
We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the…
A chain rule and a subadditivity for the entropy of type $\beta$, which is one of the nonadditive entropies, were derived by Z.Dar\'oczy. In this paper, we study the further relations among Tsallis type entropies which are typical…
The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…
We show that the non-additivity relation of the Tsallis entropies in nonextensive statistical mechanics has a simple physical interpretation for systems with fluctuating temperature or fluctuating energy dissipation rate. We also show that…
The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the…
We provide a rigorous first-principle derivation of the non-additive Tsallis' entropy by employing the Chaitin-Kolmogorov algorithmic information theory. By applying non-local restrictive rules on the string formation (grammar), we show…
In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual…
A two-parameter family of statistical measures of complexity are introduced based on the Tsallis-type nonadditive entropies. This provides a unified framework for the study of the recently proposed various measures of complexity as well as…
The pseudo-additive relation that the Tsallis entropy satisfies has nothing whatsoever to do with the super- and sub- additivity properties of the entropy. The latter properties, like concavity and convexity, are couched in geometric…
We consider statistically independent non-identical subsystems with different entropic indices q1 and q2. A relation between q1, q2 and q' (for the entire system) extends a power law for entropic index as a function of distance r. A few…
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
We discuss the idea that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…
Tsallis' non-extensive entropy $S_q$ enables us to treat both a power and exponential evolutions of underlying microscopic dynamics on equal footing by adjusting the variable entropic index $q$ to proper one $q^*$. We propose an alternative…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
The purpose of this note is to argue that degree of nonextensivity as given by Tsallis distribution obtained from maximum entropy principle has a different origin than nonextensivity inferred from pseudo-additive property of Tsallis…
In this paper we introduce an easy to compute upper bound on the Tsallis entropy of a density matrix describing a system coupled to a noise source. This suggests that the Tsallis entropy is most natural in the context of quantum information…