1,266 research outputs found

    Superstatistics Based on the Microcanonical Ensemble

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    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

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    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 qq-Entropies of Composite Quantum Systems

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    The study of conditional qq-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The qq-entropies depend on the density matrix ρ\rho through the quantity ωq=Trρq\omega_q = Tr\rho^q, and admit as a particular instance the standard von Neumann entropy in the limit case q→1q\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 qq-entropies and to their connections with other separability-related features, including the majorization condition. Different values of the entropic parameter qq are considered, as well as different values of the dimensions N1N_1 and N2N_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 qq and as a function of N1N_1 and N2N_2, of the various entropic functionals considered.Comment: Submitted for publicatio

    Entanglement and the Quantum Brachistochrone Problem

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    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