174 research outputs found
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 entropy , with , can be {\it
extensive}. More specifically, if the components of a vector are distributed according to a Gaussian probability distribution
, the associated entropy exhibits the extensivity property for
special types of correlations among the . 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 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
-generalized quantum distributions which have recently been shown to
reproduce various experimental results related to high 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 -Deformed Fermi-Dirac Distribution in Nonextensive Thermostatics
The -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 -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 of a Werner state, on
the one hand, and (ii) the temperature of the one-dimensional Heisenberg
two-spin chain with a magnetic field along the axis, on the other one.
This is true for each value of below a certain critical value . The
pertinent mapping depends on the particular 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 produced by
the Hadamard-CNOT circuit on a general (pure or mixed) state describing
a system of two qubits. We study numerically the probabilities of obtaining
different values of , 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 produced by a
unitary transformation acting on a general (pure or mixed) state
describing a system of two qubits. We study numerically the probabilities of
obtaining different values of , 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]
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