29 research outputs found

    Generalised asymptotic equivalence for extensive and non-extensive entropies

    Full text link
    We extend the Hanel and Thurner asymptotic analysis to both extensive and non-extensive entropies on the basis of a wide class of entropic forms. The procedure is known to be capable to classify multiple entropy measures in terms of their defining equivalence classes. Those are determined by a pair of scaling exponents taking into account a large number of microstates as for the thermodynamical limit. Yet, a generalisation to this formulation makes it possible to establish an entropic connection between Markovian and non-Markovian statistical systems through a set of fundamental entropies S±S_{\pm}, which have been studied in other contexts and exhibit, among their attributes, two interesting aspects: They behave as additive for a large number of degrees of freedom while they are substantially non-additive for a small number of them. Furthermore, an ample amount of special entropy measures, either additive or non-additive, are contained in such asymptotic classification. Under this scheme we analyse the equivalence classes of Tsallis, Sharma-Mittal and R\'enyi entropies and study their features in the thermodynamic limit as well as the correspondences among them.Comment: 6 pages, 2 figure

    Interacting Tsallis holographic dark energy in qq-modified DGP braneworld

    Full text link
    We explore the cosmological aspects of interacting Tsallis holographic dark energy (THDE) in a qq-modified DGP braneworld setup emerging from non-Gaussian statistical mechanics.To this end, three classes of superstatistics, that is, log-normal, inverse χ2\chi^2 and χ2\chi^2 superstatistics were incorporated into the model. We examined the implication of the three superstatistics on different cosmological parameters, namely, the dimensionless energy density and the equation-of-state (EoS) of THDE, along with the deceleration parameter and the squared speed of sound. As a result, we noted that the cosmological parameters stemming from the χ2\chi^2 superstatistics, with a parameter q>1q > 1, represent the highest deviation from those ascribed to the standard DGP model. While the system parameters show appropriate behavior in all three cases, the model cannot achieve stability throughout the history of the Universe. It is probably the outcome of setting the Hubble horizon as the infrared cutoff. Furthermore, the behavior of EoS was found to be governed by the value of the THDE parameter δ{\delta}. That is to say, for δ>2{\delta} > 2 THDE exhibits a phantom-like behavior while for δ<2{\delta} < 2 it displays a quintessence behavior. Constrained by the dominant energy condition, an upper bound on δ{\delta} (δ<2)({\delta} < 2) has been imposed

    Generalized entropy arising from a distribution of q-indices

    Full text link
    It is by now well known that the Boltzmann-Gibbs (BG) entropy SBG=ki=1WpilnpiS_{BG}=-k\sum_{i=1}^W p_i \ln p_i can be usefully generalized into the entropy Sq=k(1i=1Wpiq)/(q1)S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1) (qR;S1=SBGq\in \mathcal{R}; S_1=S_{BG}). Microscopic dynamics determines, given classes of initial conditions, the occupation of the accessible phase space (or of a symmetry-determined nonzero-measure part of it), which in turn appears to determine the entropic form to be used. This occupation might be a uniform one (the usual {\it equal probability hypothesis} of BG statistical mechanics), which corresponds to q=1q=1; it might be a free-scale occupancy, which appears to correspond to q1q \ne 1. Since occupancies of phase space more complex than these are surely possible in both natural and artificial systems, the task of further generalizing the entropy appears as a desirable one, and has in fact been already undertaken in the literature. To illustrate the approach, we introduce here a quite general entropy based on a distribution of qq-indices thus generalizing SqS_q. We establish some general mathematical properties for the new entropic functional and explore some examples. We also exhibit a procedure for finding, given any entropic functional, the qq-indices distribution that produces it. Finally, on the road to establishing a quite general statistical mechanics, we briefly address possible generalized constraints under which the present entropy could be extremized, in order to produce canonical-ensemble-like stationary-state distributions for Hamiltonian systems.Comment: 14 pages including 3 figure

    The emergence of Special and Doubly Special Relativity

    Full text link
    Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. This can be described in terms of polycrystalline vacuum. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. By analyzing the robustness of such a special relativity under small variations in the polycrystalline grain-size distribution we naturally arrive at the notion of doubly-special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as the role of gauge fixing in emergent relativity, generalized commutation relations, Hausdorff dimensions of representative path-integral trajectories and a connection with Feynman chessboard model are also discussed.Comment: 21 pages, 1 figure, RevTeX4, substantially revised version, accepted in Phys. Rev.

    On superstatistics and black hole quasinormal modes

    Full text link
    It is known that one can determine that lowest value of spin is jmin=1j_{min}=1, by using the quasinormal modes of black holes, the Bekenstein-Hawking entropy and Boltzmann-Gibbs statistics. In this paper, to determine jminj_{min}, we have used non extensive entropies that depend only on the probability (known as Obregon's entropies and have been derived from superstatistics), as well as non extensive entropies that have free parameters . We find that jminj_{min} depends on the area and the non extensive parameter. In particular, for the non extensive entropies that only depend on the probability and find that the modification is only present for micro black holes. For classical black holes, the results are the same as for the Boltzmann-Gibbs statistics.Comment: 8 pages, 4 figure
    corecore