Correlated Gaussian systems exhibiting additive power-law entropies

We show, on purely statistical grounds and without appeal to any physical model, that a power-law $q-$entropy $S_q$, with $0<q<1$, can be {\it extensive}. More specifically, if the components $X_i$ of a vector $X \in \mathbb{R}^N$ are distributed according to a Gaussian probability distribution $f$, the associated entropy $S_q(X)$ exhibits the extensivity property for special types of correlations among the $X_i$. We also characterize this kind of correlation.Comment: 2 figure

How fundamental is the character of thermal uncertainty relations?

We show that thermodynamic uncertainties do not preserve their form if the underlying probability distribution is transformed into an escort one. Heisenberg's relations, on the other hand, are not affected by such transformation. We conclude therefore that the former uncertainty cannot be as fundamental as the quantum one.Comment: 4 pages, no figure

On the Cut-Off Prescriptions Associated with Power-Law Generalized Thermostatistics

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 discuss some of its basic mathematical properties. As an illustration of the new cut-off prescription we consider in some detail the $q$-generalized quantum distributions which have recently been shown to reproduce various experimental results related to high $T_c$ superconductors

Numerical Determination of the Distribution of Energies for the XY-model

We compute numerically the distribution of energies W(E,N) for the XY-model with short-range and long-range interactions. We find that in both cases the distribution can be fitted to the functional form: W(E,N) ~ exp(N f(E,N)), with f(E,N) an intensive function of the energy.Comment: 4 pages, 1 figure. Submitted to Physica

Thermodynamic Consistency of the qq-Deformed Fermi-Dirac Distribution in Nonextensive Thermostatics

The $q$-deformed statistics for fermions arising within the non-extensive thermostatistical formalism has been applied to the study of various quantum many-body systems recently. The aim of the present note is to point out some subtle difficulties presented by this approach in connection with the problem of thermodynamic consistency. Different possible ways to apply the $q$-deformed quantum distributions in a thermodynamically consistent way are considered.Comment: 4 pages, 1 figur

Entropic Upper Bound on Gravitational Binding Energy

We prove that the gravitational binding energy {\Omega} of a self gravitating system described by a mass density distribution {\rho}(x) admits an upper bound B[{\rho}(x)] given by a simple function of an appropriate, non-additive Tsallis' power-law entropic functional Sq evaluated on the density {\rho}. The density distributions that saturate the entropic bound have the form of isotropic q-Gaussian distributions. These maximizer distributions correspond to the Plummer density profile, well known in astrophysics. A heuristic scaling argument is advanced suggesting that the entropic bound B[{\rho}(x)] is unique, in the sense that it is unlikely that exhaustive entropic upper bounds not based on the alluded Sq entropic measure exit. The present findings provide a new link between the physics of self gravitating systems, on the one hand, and the statistical formalism associated with non-additive, power-law entropic measures, on the other hand

Werner states and the two-spinors Heisenberg anti-ferromagnet

We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys. Rev. Lett. {\bf 87} (2001) 017901] and using the statistical tool called {\it entropic non-triviality} [Lamberti, Martin, Plastino, and Rosso, Physica A {\bf 334} (2004) 119], that there is a one to one correspondence between (i) the mixing coefficient $x$ of a Werner state, on the one hand, and (ii) the temperature $T$ of the one-dimensional Heisenberg two-spin chain with a magnetic field $B$ along the $z-$axis, on the other one. This is true for each value of $B$ below a certain critical value $B_c$. The pertinent mapping depends on the particular $B-$value one selects within such a range

The statistics of the entanglement changes generated by the Hadamard-CNOT quantum circuit

We consider the change of entanglement of formation $\Delta E$ produced by the Hadamard-CNOT circuit on a general (pure or mixed) state $\rho$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $\Delta E$, assuming that the initial state is randomly distributed in the space of all states according to the product measure recently introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998) 883].Comment: 12 pages, 2 figure

On the distribution of entanglement changes produced by unitary operations

We consider the change of entanglement of formation $\Delta E$ produced by a unitary transformation acting on a general (pure or mixed) state $\rho$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $\Delta E$, assuming that the initial state is randomly distributed in the space of all states according to the product measure introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998) 883]