60 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
On a conjecture about Dirac's delta representation using q-exponentials
A new representation of Dirac's delta-distribution, based on the so-called
q-exponentials, has been recently conjectured. We prove here that this
conjecture is indeed valid
The q-exponential family in statistical physics
The notion of generalised exponential family is considered in the restricted
context of nonextensive statistical physics. Examples are given of models
belonging to this family. In particular, the q-Gaussians are discussed and it
is shown that the configurational probability distributions of the
microcanonical ensemble belong to the q-exponential family.Comment: 18 pages, 4 figures, proceedings of SigmaPhi 200
Form Sequences to Polynomials and Back, via Operator Orderings
C.M. Bender and G. V. Dunne showed that linear combinations of words
, where and are subject to the relation , may be expressed as a polynomial in the symbol . Relations between such polynomials and linear
combinations of the transformed coefficients are explored. In particular,
examples yielding orthogonal polynomials are provided
Strictly and asymptotically scale-invariant probabilistic models of correlated binary random variables having {\em q}--Gaussians as limiting distributions
In order to physically enlighten the relationship between {\it
--independence} and {\it scale-invariance}, we introduce three types of
asymptotically scale-invariant probabilistic models with binary random
variables, namely (i) a family, characterized by an index ,
unifying the Leibnitz triangle () and the case of independent variables
(); (ii) two slightly different discretizations of
--Gaussians; (iii) a special family, characterized by the parameter ,
which generalizes the usual case of independent variables (recovered for
). Models (i) and (iii) are in fact strictly scale-invariant. For
models (i), we analytically show that the probability
distribution is a --Gaussian with . Models (ii) approach
--Gaussians by construction, and we numerically show that they do so with
asymptotic scale-invariance. Models (iii), like two other strictly
scale-invariant models recently discussed by Hilhorst and Schehr (2007),
approach instead limiting distributions which are {\it not} --Gaussians. The
scenario which emerges is that asymptotic (or even strict) scale-invariance is
not sufficient but it might be necessary for having strict (or asymptotic)
--independence, which, in turn, mandates --Gaussian attractors.Comment: The present version is accepted for publication in JSTA
Consequences of temperature fluctuations in observables measured in high energy collisions
We review the consequences of intrinsic, nonstatistical temperature
fluctuations as seen in observables measured in high energy collisions. We do
this from the point of view of nonextensive statistics and Tsallis
distributions. Particular attention is paid to multiplicity fluctuations as a
first consequence of temperature fluctuations, to the equivalence of
temperature and volume fluctuations, to the generalized thermodynamic
fluctuations relations allowing us to compare fluctuations observed in
different parts of phase space, and to the problem of the relation between
Tsallis entropy and Tsallis distributions. We also discuss the possible
influence of conservation laws on these distributions and provide some examples
of how one can get them without considering temperature fluctuations.Comment: Revised version of the invited contribution to The European Physical
Journal A (Hadrons and Nuclei) topical issue about 'Relativistic Hydro- and
Thermodynamics in Nuclear Physics' guest eds. Tamas S. Biro, Gergely G.
Barnafoldi and Peter Va
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