Related papers: Some remarks on Tsallis relative operator entropy

We investigate weighted inequalities for fractional maximal operators and fractional integral operators. We work within the innovative framework of "entropy bounds" introduced by Treil--Volberg. Using techniques developed by Lacey and the…

We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \quad z \in \ol \Sigma = \{z\in\bbC\,|\, \Re(z) \in [0,1]\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$.…

We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore…

Bento \textit{et al.} [Phys. Rev. E 91, 022105 (2015)] recently stated that the Tsallis entropy violates the third law of thermodynamics for $0 < q <1$ in the sub-additive regime. We first show that the division between the regimes $q < 1$…

We prove that the realization $A_p$ in $L^p(\mathbb{R}^N),\,1<p<\infty$, of the elliptic operator $A=(1+|x|^{\alpha})\Delta+b|x|^{\alpha-1}\frac{x}{|x|}\cdot \nabla-c|x|^{\beta}$ with domain $D(A_p) =\{ u \in W^{2,p}(\mathbb{R}^N)\, |\, Au…

We have studied finite $N$-body $D$-dimensional nonextensive ideal gases and harmonic oscillators, by using the maximum-entropy methods with the $q$- and normal averages ($q$: the entropic index). The validity range, specific heat and…

Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannons entropy is just the size of the sample space when the distribution is uniform.…

We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…

Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into…

We gave a simple derivation of density operator with the quantum analysis. We dealt with the functional of a density operator, and applied maximum entropy principle. We obtained easily the density operators for the Tsallis entropy and…

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…

This article extends the non-extensive entropy of Tsallis and uses this entropy to model an energy producing system in an absorbing heat bath. This modified non-extensive entropy is superficially identical to the one proposed by Tsallis,…

In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al. [cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis' entropy to…

In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation valu of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort…

We first observe that the (co)domains of the q-deformed functions are some subsets of the (co)domains of their ordinary counterparts, thereby deeming the deformed functions to be incomplete. In order to obtain a complete definition of…

Traditional thermodynamic trade-off relations usually apply to quantities that depend linearly on probability distributions. In contrast, many important information-theoretic measures, such as entropies, are nonlinear and therefore…

In this paper we derived a 6N dimensional non-homogeneous evolution equation of Tsallis non-equilibrium entropy; presented a formula for entropy production rate (i.e. the law of entropy increase) for Tsallis entropy only when its index q>0,…

This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…

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…

We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden-Thompson's trace inequality…