1,018 research outputs found
Microscopic dynamics underlying the anomalous diffusion
The time dependent Tsallis statistical distribution describing anomalous
diffusion is usually obtained in the literature as the solution of a non-linear
Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347
(1995)]. The scope of the present paper is twofold. Firstly we show that this
distribution can be obtained also as solution of the non-linear porous media
equation. Secondly we prove that the time dependent Tsallis distribution can be
obtained also as solution of a linear FP equation [G. Kaniadakis and P.
Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the
velocity, that describes a generalized Brownian motion. This linear FP equation
is shown to arise from a microscopic dynamics governed by a standard Langevin
equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200
Ferromagnetic material in the eastern red-spotted newt notophthalmus viridescens
Behavioral results obtained from the eastern red-spotted newt (Notophthalmus viridescens) led to the suggestion of a hybrid homing system involving inputs from both a light-dependent and a non-light-dependent mechanism. To evaluate the possible role of a receptor based on biogenic magnetite in this animal, we performed magnetometry experiments on a set of newts previously used in behavioral assays. The natural remanent magnetization (NRM) carried by these newts was strong enough to be measured easily using a direct-current-biased superconducting quantum interference device functioning as a moment magnetometer. Isothermal remanent magnetizations were two orders of magnitude higher than the NRM, suggesting that ferromagnetic material consistent with magnetite is present in the body of the newt. The NRM has no preferential orientation among the animals when analyzed relative to their body axis, and the demagnetization data show that, overall, the magnetic material grains are not aligned parallel to each other within each newt. Although the precise localization of the particles was not possible, the data indicate that magnetite is not clustered in a limited area. A quantity of single-domain magnetic material is present which would be adequate for use in either a magnetic intensity or direction receptor. Our data, when combined with the functional properties of homing, suggest a link between this behavioral response and the presence of ferromagnetic material, raising the possibility that magnetite is involved at least in the map component of homing of the eastern red-spotted newt
Geometry of escort distributions
Given an original distribution, its statistical and probabilistic attributs
may be scanned by the associated escort distribution introduced by Beck and
Schlogl and employed in the formulation of nonextensive statistical mechanics.
Here, the geometric structure of the one-parameter family of the escort
distributions is studied based on the Kullback-Leibler divergence and the
relevant Fisher metric. It is shown that the Fisher metric is given in terms of
the generalized bit-variance, which measures fluctuations of the crowding index
of a multifractal. The Cramer-Rao inequality leads to the fundamental limit for
precision of statistical estimate of the order of the escort distribution. It
is also quantitatively discussed how inappropriate it is to use the original
distribution instead of the escort distribution for calculating the expectation
values of physical quantities in nonextensive statistical mechanics.Comment: 12 pages, no figure
Nonextensive Entropies derived from Form Invariance of Pseudoadditivity
The form invariance of pseudoadditivity is shown to determine the structure
of nonextensive entropies. Nonextensive entropy is defined as the appropriate
expectation value of nonextensive information content, similar to the
definition of Shannon entropy. Information content in a nonextensive system is
obtained uniquely from generalized axioms by replacing the usual additivity
with pseudoadditivity. The satisfaction of the form invariance of the
pseudoadditivity of nonextensive entropy and its information content is found
to require the normalization of nonextensive entropies. The proposed principle
requires the same normalization as that derived in [A.K. Rajagopal and S. Abe,
Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis
for the systematic definition of various entropies in nonextensive systems.Comment: 16 pages, accepted for publication in Physical Review
Information Theory based on Non-additive Information Content
We generalize the Shannon's information theory in a nonadditive way by
focusing on the source coding theorem. The nonadditive information content we
adopted is consistent with the concept of the form invariance structure of the
nonextensive entropy. Some general properties of the nonadditive information
entropy are studied, in addition, the relation between the nonadditivity
and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev.
E(an error in proof of theorem 1 was corrected, typos corrected
Multiplicative noise: A mechanism leading to nonextensive statistical mechanics
A large variety of microscopic or mesoscopic models lead to generic results
that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based
on ). Similarly, other classes of models
point toward nonextensive statistical mechanics (based on , where the value of the entropic index depends on
the specific model). We show here a family of models, with multiplicative
noise, which belongs to the nonextensive class. More specifically, we consider
Langevin equations of the type , where
and are independent zero-mean Gaussian white noises with
respective amplitudes and . This leads to the Fokker-Planck equation
. Whenever the
deterministic drift is proportional to the noise induced one, i.e., , the stationary solution is shown to be (with and ). This distribution is
precisely the one optimizing with the constraint constant. We also
introduce and discuss various characterizations of the width of the
distributions.Comment: 3 PS figure
Anomalous diffusion and Tsallis statistics in an optical lattice
We point out a connection between anomalous quantum transport in an optical
lattice and Tsallis' generalized thermostatistics. Specifically, we show that
the momentum equation for the semiclassical Wigner function that describes
atomic motion in the optical potential, belongs to a class of transport
equations recently studied by Borland [PLA 245, 67 (1998)]. The important
property of these ordinary linear Fokker--Planck equations is that their
stationary solutions are exactly given by Tsallis distributions. Dissipative
optical lattices are therefore new systems in which Tsallis statistics can be
experimentally studied.Comment: 4 pages, 1 figur
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
Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution
The nonlinear diffusion equation is analyzed here, where , and , and are real parameters.
This equation unifies the anomalous diffusion equation on fractals ()
and the spherical anomalous diffusion for porous media (). Exact
point-source solution is obtained, enabling us to describe a large class of
subdiffusion (), normal diffusion () and
superdiffusion (). Furthermore, a thermostatistical basis
for this solution is given from the maximum entropic principle applied to the
Tsallis entropy.Comment: 3 pages, 2 eps figure
Quantum entanglement inferred by the principle of maximum Tsallis entropy
The problem of quantum state inference and the concept of quantum
entanglement are studied using a non-additive measure in the form of Tsallis
entropy indexed by the positive parameter q. The maximum entropy principle
associated with this entropy along with its thermodynamic interpretation are
discussed in detail for the Einstein-Podolosky-Rosen pair of two spin-1/2
particles. Given the data on the Bell-Clauser-Horne-Shimony-Holt observable,
the analytic expression is given for the inferred quantum entangled state. It
is shown that for q greater than unity, indicating the sub-additive feature of
the Tsalls entropy, the entangled region is small and enlarges as one goes into
super-additive regime where q is less than unity. It is also shown that quantum
entanglement can be quantified by the generalized Kullback-Leibler entropy.Comment: 15 pages, 1 figur
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