Related papers: Tsallis relative operator entropy in mathematical …
In an attempt to understand the Tsallis entropy composition property, we construct an embedding of the reals into the set of $3\times 3$ upper triangular matrices with real entries. We explore consequences of this embedding and of the…
We show that there exists a natural way to define a condition of generalized thermal equilibrium between systems governed by Tsallis thermostatistics, under the hypotheses that i) the coupling between the systems is weak, ii) the structure…
In previous work (see arxiv:1102.3040), we have defined the telescopic relative entropy (TRE), which is a regularisation of the quantum relative entropy $S(\rho||\sigma)=\trace\rho(\log\rho-\log\sigma)$, by replacing the second argument…
We introduce a fractional generalization of Tsallis entropy by acting with a $q$-Caputo operator on the generating family $\sum_i p_i^{\,x}$ evaluated at $x=1$. Concretely, we define $S_{q}^{\alpha}$ through the $q$-Caputo differintegral of…
We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…
The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari, IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the generalized Shannon-Khinchin's axiom. In the present paper, this result is generalized…
We discuss a Tsallis distribution with complex nonextensivity parameter $q$. In this case the usual distribution is decorated with a log-periodic oscillating factor (apparently, such oscillations can bee seen in recently measured transverse…
It is natural important question for us to ask what the nonextensive parameter stands for when Tsallis statistics is applied to the self-gravitating systems. In this paper, some properties of the nonextensive parameter and Tsallis…
We study the applications of non-extensive Tsallis statistics to high energy and hadron physics. These applications include studies of $pp$ collisions, equation of state of QCD, as well as Bose-Einstein condensation. We also analyze the…
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon…
The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
We expand the Tsallis distribution in a Taylor series of powers of (q-1), where q is the Tsallis parameter, assuming q is very close to 1. This helps in studying the degree of deviation of transverse momentum spectra and other thermodynamic…
It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.
R\'enyi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the R\'enyi entropy are not widely known. In this paper,…
We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the…
Two important problems existing in Tsallis' statistics are investigated, where one is whether energy is extensive or not, and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not.…
We revisit the cut-off prescriptions which are needed in order to specify completely the form of Tsallis' maximum entropy distributions. For values of the Tsallis entropic parameter $q>1$ we advance an alternative cut-off prescription and…
By writing total Tsallis entropy as a function of non-extensivity q-parameter withing the fragment-asperity model for earthquakes, a critical range of values is identified: 1.4 <q< 1.8. It comes directly from constructing the non-extensive…
The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function.…