Related papers: Reconciliation between the Tsallis maximum entropy…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
It is shown that the R\'enyi and Tsallis entropies and the q-expectation values, are continuous and stable if $q>1$ and are not continuous and instable for uniform finite distributions if $q<1$.
I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic…
We provide a unifying axiomatics for Renyi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszar's measure of directed divergence known from communication theory.
The common cause principle for two random variables $A$ and $B$ is examined in the case of causal insufficiency, when their common cause $C$ is known to exist, but only the joint probability of $A$ and $B$ is observed. As a result, $C$…
We explore properties of the $\chi^2$ and more general R\'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
I show that the maximum entropy principle can be replaced by a more natural assumption, that there exists a phenomenological function of entropy consistent with the microscopic model. The requirement of existence provides then a unique…
Microcanonical equations for several thermodynamic properties of a system, suitable for molecular dynamics simulations, are derived from the nonextensive Tsallis entropy functional. Two possible definitions of temperature, the usual one and…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
We have obtained the Tsallis distribution from the maximum entropy approach using constraints on the first and the second moment, together with the normalization condition. We have constructed railway and highway communication networks for…
We adapt the Kolmogorov-Sinai entropy to the non-extensive perspective recently advocated by Tsallis. The resulting expression is an average on the invariant distribution, which should be used to detect the genuine entropic index Q. We…
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…
Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc's for the a.s. convergence of series of an…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
By using the maximum entropy principle, with Tsallis entropy, we obtain an explicit dependence for energy distribution of earthquakes. This function describes very well the observations in a wide range of energies, where other distribution…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…