23,528 research outputs found
Macroscopic thermodynamics of equilibrium characterized by power-law canonical distributions
Macroscopic thermodynamics of equilibrium is constructed for systems obeying
power-law canonical distributions. With this, the connection between
macroscopic thermodynamics and microscopic statistical thermodynamics is
generalized. This is complementary to the Gibbs theorem for the celebrated
exponential canonical distributions of systems in contact with a heat bath.
Thereby, a thermodynamic basis is provided for power-law phenomena ubiquitous
in nature.Comment: 12 page
Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions
The q-exponential distributions, which are generalizations of the
Zipf-Mandelbrot power-law distribution, are frequently encountered in complex
systems at their stationary states. From the viewpoint of the principle of
maximum entropy, they can apparently be derived from three different
generalized entropies: the Renyi entropy, the Tsallis entropy, and the
normalized Tsallis entropy. Accordingly, mere fittings of observed data by the
q-exponential distributions do not lead to identification of the correct
physical entropy. Here, stabilities of these entropies, i.e., their behaviors
under arbitrary small deformation of a distribution, are examined. It is shown
that, among the three, the Tsallis entropy is stable and can provide an
entropic basis for the q-exponential distributions, whereas the others are
unstable and cannot represent any experimentally observable quantities.Comment: 20 pages, no figures, the disappeared "primes" on the distributions
are added. Also, Eq. (65) is correcte
B Physics at SLD
We review recent physics results obtained in polarized
interactions at the SLC by the SLD experiment. The excellent 3-D vertexing
capabilities of SLD are exploited to extract precise \bu and \bd lifetimes,
as well as measurements of the time evolution of mixing.Comment: 7 pages, 4 figure
Dynamical evolution of clustering in complex network of earthquakes
The network approach plays a distinguished role in contemporary science of
complex systems/phenomena. Such an approach has been introduced into seismology
in a recent work [S. Abe and N. Suzuki, Europhys. Lett. 65, 581 (2004)]. Here,
we discuss the dynamical property of the earthquake network constructed in
California and report the discovery that the values of the clustering
coefficient remain stationary before main shocks, suddenly jump up at the main
shocks, and then slowly decay following a power law to become stationary again.
Thus, the network approach is found to characterize main shocks in a peculiar
manner.Comment: 10 pages, 3 figures, 1 tabl
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
Scale-invariant statistics of period in directed earthquake network
A new law regarding structure of the earthquake networks is found. The
seismic data taken in California is mapped to a growing directed network. Then,
statistics of period in the network, which implies that after how many
earthquakes an earthquake returns to the initial location, is studied. It is
found that the period distribution obeys a power law, showing the fundamental
difficulty of statistical estimate of period.Comment: 11 pages including 3 figure
Microcanonical Foundation for Systems with Power-Law Distributions
Starting from microcanonical basis with the principle of equal a priori
probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the
exponential distribution, a theory describing systems with power-law
distributions can also be derived.Comment: 9 page
Nonadditive measure and quantum entanglement in a class of mixed states of N^n-system
Through the generalization of Khinchin's classical axiomatic foundation, a
basis is developed for nonadditive information theory. The classical
nonadditive conditional entropy indexed by the positive parameter q is
introduced and then translated into quantum information. This quantity is
nonnegative for classically correlated states but can take negative values for
entangled mixed states. This property is used to study quantum entanglement in
the parametrized Werner-Popescu-like state of an N^n-system, that is, an
n-partite N-level system. It is shown how the strongest limitation on validity
of local realism (i.e., separability of the state) can be obtained in a novel
manner
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