908 research outputs found
Superstatistics Based on the Microcanonical Ensemble
Superstatistics is a "statistics" of "canonical-ensemble statistics". In
analogy, we consider here a similar theoretical construct, but based upon the
microcanonical ensemble. The mixing parameter is not the temperature but the
index q associated with the non-extensive, power law entropy Sq.Comment: 10 pages, 3 figure
Poincar\'{e}'s Observation and the Origin of Tsallis Generalized Canonical Distributions
In this paper, we present some geometric properties of the maximum entropy
(MaxEnt) Tsallis- distributions under energy constraint. In the case q > 1,
these distributions are proved to be marginals of uniform distributions on the
sphere; in the case q < 1, they can be constructed as conditional distribu-
tions of a Cauchy law built from the same uniform distribution on the sphere
using a gnomonic projection. As such, these distributions reveal the relevance
of using Tsallis distributions in the microcanonical setup: an example of such
application is given in the case of the ideal gas.Comment: 2 figure
Density operators that extremize Tsallis entropy and thermal stability effects
Quite general, analytical (both exact and approximate) forms for discrete
probability distributions (PD's) that maximize Tsallis entropy for a fixed
variance are here investigated. They apply, for instance, in a wide variety of
scenarios in which the system is characterized by a series of discrete
eigenstates of the Hamiltonian. Using these discrete PD's as "weights" leads to
density operators of a rather general character. The present study allows one
to vividly exhibit the effects of non-extensivity. Varying Tsallis'
non-extensivity index one is seen to pass from unstable to stable systems
and even to unphysical situations of infinite energy.Comment: 22 page
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
Entanglement and the Quantum Brachistochrone Problem
Entanglement is closely related to some fundamental features of the dynamics
of composite quantum systems: quantum entanglement enhances the "speed" of
evolution of certain quantum states, as measured by the time required to reach
an orthogonal state. The concept of "speed" of quantum evolution constitutes an
important ingredient in any attempt to determine the fundamental limits that
basic physical laws impose on how fast a physical system can process or
transmit information. Here we explore the relationship between entanglement and
the speed of quantum evolution in the context of the quantum brachistochrone
problem. Given an initial and a final state of a composite system we consider
the amount of entanglement associated with the brachistochrone evolution
between those states, showing that entanglement is an essential resource to
achieve the alluded time-optimal quantum evolution.Comment: 6 pages, 3 figures. Corrected typos in Eqs. 1 and
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