1,266 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

### Some Features of the Conditional $q$-Entropies of Composite Quantum Systems

The study of conditional $q$-entropies in composite quantum systems has
recently been the focus of considerable interest, particularly in connection
with the problem of separability. The $q$-entropies depend on the density
matrix $\rho$ through the quantity $\omega_q = Tr\rho^q$, and admit as a
particular instance the standard von Neumann entropy in the limit case $q\to
1$. A comprehensive numerical survey of the space of pure and mixed states of
bipartite systems is here performed, in order to determine the volumes in state
space occupied by those states exhibiting various special properties related to
the signs of their conditional $q$-entropies and to their connections with
other separability-related features, including the majorization condition.
Different values of the entropic parameter $q$ are considered, as well as
different values of the dimensions $N_1$ and $N_2$ of the Hilbert spaces
associated with the constituting subsystems. Special emphasis is paid to the
analysis of the monotonicity properties, both as a function of $q$ and as a
function of $N_1$ and $N_2$, of the various entropic functionals considered.Comment: Submitted for publicatio

### 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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