29 research outputs found
Generalised asymptotic equivalence for extensive and non-extensive entropies
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
, 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 -modified DGP braneworld
We explore the cosmological aspects of interacting Tsallis holographic dark
energy (THDE) in a -modified DGP braneworld setup emerging from non-Gaussian
statistical mechanics.To this end, three classes of superstatistics, that is,
log-normal, inverse and 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 superstatistics, with a parameter , 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 . That is to say, for
THDE exhibits a phantom-like behavior while for it displays a
quintessence behavior. Constrained by the dominant energy condition, an upper
bound on has been imposed
Generalized entropy arising from a distribution of q-indices
It is by now well known that the Boltzmann-Gibbs (BG) entropy
can be usefully generalized into the
entropy (). 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 ; it might be a free-scale occupancy, which appears
to correspond to . 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 -indices
thus generalizing . 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 -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
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
It is known that one can determine that lowest value of spin is ,
by using the quasinormal modes of black holes, the Bekenstein-Hawking entropy
and Boltzmann-Gibbs statistics. In this paper, to determine , 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 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