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

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

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 $q$ one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy.Comment: 22 page