201,897 research outputs found
Extended quasi-additivity of Tsallis entropies
We consider statistically independent non-identical subsystems with different
entropic indices q1 and q2. A relation between q1, q2 and q' (for the entire
system) extends a power law for entropic index as a function of distance r. A
few examples illustrate a role of the proposed constraint q' < min(q1, q2) for
the Beck's concept of quasi-additivity.Comment: to appear in Physica
Modelling train delays with q-exponential functions
We demonstrate that the distribution of train delays on the British railway
network is accurately described by q-exponential functions. We explain this by
constructing an underlying superstatistical model.Comment: 12 pages, 5 figure
Generalized statistical mechanics of cosmic rays
We consider a generalized statistical mechanics model for the creation
process of cosmic rays which takes into account local temperature fluctuations.
This model yields Tsallis statistics for the cosmic ray spectrum. It predicts
an entropic index q given by q=11/9 at largest energies (equivalent to a
spectral index of alpha=5/2), and an effective temperature given by (5/9)T_H,
where kT_H approximately equal to 180 MeV is the Hagedorn temperature measured
in collider experiments. Our theoretically obtained formula is in very good
agreement with the experimentally measured energy spectrum of primary cosmic
rays.Comment: 10 pages, 2 figure
Generalized statistical mechanics and fully developed turbulence
The statistical properties of fully developed hydrodynamic turbulence can be
successfully described using methods from nonextensive statistical mechanics.
The predicted probability densities and scaling exponents precisely coincide
with what is measured in various turbulence experiments. As a dynamical basis
for nonextensive behaviour we consider nonlinear Langevin equations with
fluctuating friction forces, where Tsallis statistics can be rigorously proved.Comment: 10 pages, 4 figures. To appear in Physica A (Proceedings of Statphys
21
Axiomatic approach to the cosmological constant
A theory of the cosmological constant Lambda is currently out of reach.
Still, one can start from a set of axioms that describe the most desirable
properties a cosmological constant should have. This can be seen in certain
analogy to the Khinchin axioms in information theory, which fix the most
desirable properties an information measure should have and that ultimately
lead to the Shannon entropy as the fundamental information measure on which
statistical mechanics is based. Here we formulate a set of axioms for the
cosmological constant in close analogy to the Khinchin axioms, formally
replacing the dependency of the information measure on probabilities of events
by a dependency of the cosmological constant on the fundamental constants of
nature. Evaluating this set of axioms one finally arrives at a formula for the
cosmological constant that is given by Lambda = (G^2/hbar^4) (m_e/alpha_el)^6,
where G is the gravitational constant, m_e is the electron mass, and alpha_el
is the low energy limit of the fine structure constant. This formula is in
perfect agreement with current WMAP data. Our approach gives physical meaning
to the Eddington-Dirac large number hypothesis and suggests that the observed
value of the cosmological constant is not at all unnatural.Comment: 7 pages, no figures. Some further references adde
Multifractal analysis of nonhyperbolic coupled map lattices: Application to genomic sequences
Symbolic sequences generated by coupled map lattices (CMLs) can be used to
model the chaotic-like structure of genomic sequences. In this study it is
shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a
shift of 4 symbols) very closely reproduce the multifractal spectrum of
human genomic sequences for coupling constant if .
The presence of rare configurations causes deviations for , which
disappear if the rare event statistics of the CML is modified. Such rare
configurations are known to play specific functional roles in genomic sequences
serving as promoters or regulatory elements.Comment: 7 pages, 6 picture
Superstatistics
We consider nonequilibrium systems with complex dynamics in stationary states
with large fluctuations of intensive quantities (e.g. the temperature, chemical
potential, or energy dissipation) on long time scales. Depending on the
statistical properties of the fluctuations, we obtain different effective
statistical mechanics descriptions. Tsallis statistics is one, but other
classes of generalized statistics are obtained as well. We show that for small
variance of the fluctuations all these different statistics behave in a
universal way.Comment: 12 pages /a few more references and comments added in revised versio
Stretched exponentials from superstatistics
Distributions exhibiting fat tails occur frequently in many different areas
of science. A dynamical reason for fat tails can be a so-called
superstatistics, where one has a superposition of local Gaussians whose
variance fluctuates on a rather large spatio-temporal scale. After briefly
reviewing this concept, we explore in more detail a class of superstatistics
that hasn't been subject of many investigations so far, namely superstatistics
for which a suitable power beta^eta of the local inverse temperature beta is
chi^2-distributed. We show that eta >0 leads to power law distributions, while
eta <0 leads to stretched exponentials. The special case eta=1 corresponds to
Tsallis statistics and the special case eta=-1 to exponential statistics of the
square root of energy. Possible applications for granular media and
hydrodynamic turbulence are discussed.Comment: 10 pages. Proceedings of NEXT-SigmaPhi conference, Kolymbari, 13-18
August 200
Chaotic quantization and the mass spectrum of fermions
In order to understand the parameters of the standard model of electroweak
and strong interactions, one needs to embed the standard model into some larger
theory that accounts for the observed values. This means some additional sector
is needed that fixes and stabilizes the values of the fundamental constants of
nature. We describe how such a sector can be constructed using the so-called
chaotic quantization method applied to a system of coupled map lattices. We
restrict ourselves in this short note on verifying how our model correctly
yields the numerical values of Yukawa and gravitational coupling constants of a
collection of heavy and light fermions using a simple principle, the local
minimization of vacuum energy.Comment: 8 pages, 6 figures. To appear in Chaos, Solitons and Fractals (2008
The --matrix action of untwisted affine quantum groups at roots of 1
Let be an untwisted affine Kac-Moody algebra. The quantum
group (over ) is known to be a
quasitriangular Hopf algebra: in particular, it has a universal --matrix,
which yields an --matrix for each pair of representations of
. On the other hand, the quantum group
(over ) also has an --matrix for each pair of
representations, but it has not a universal --matrix so that one cannot
say that it is quasitriangular. Following Reshetikin, one introduces the
(weaker) notion of braided Hopf algebra: then is a
braided Hopf algebra.
In this work we prove that also the unrestricted specializations of
at roots of 1 are braided: in particular, specializing
at 1 we have that the function algebra of the Poisson
proalgebraic group dual of (a Kac-Moody group with Lie
algebra ) is braided. This is useful because, despite these
specialized quantum groups are not quasitriangular, the braiding is enough for
applications, mainly for producing knot invariants. As an example, the action
of the --matrix on (tensor products of) Verma modules can be specialized
at odd roots of 1.Comment: 12 pages, AMS-TeX C, Version 2.1c - this is the author's file of the
final version (after the refereeing process), as sent for publicatio
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