19,635 research outputs found

### 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

### 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

### Generalized entropies and the transformation group of superstatistics

Superstatistics describes statistical systems that behave like superpositions
of different inverse temperatures $\beta$, so that the probability distribution
is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta
\epsilon_i}d\beta$, where the `kernel' $f(\beta)$ is nonnegative and normalized
($\int f(\beta)d \beta =1$). We discuss the relation between this distribution
and the generalized entropic form $S=\sum_i s(p_i)$. The first three
Shannon-Khinchin axioms are assumed to hold. It then turns out that for a given
distribution there are two different ways to construct the entropy. One
approach uses escort probabilities and the other does not; the question of
which to use must be decided empirically. The two approaches are related by a
duality. The thermodynamic properties of the system can be quite different for
the two approaches. In that connection we present the transformation laws for
the superstatistical distributions under macroscopic state changes. The
transformation group is the Euclidean group in one dimension.Comment: 5 pages, no figur

### Rapidity Gaps from Colour String Topologies

Diffractive deep inelastic scattering at HERA and diffractive W and jet
production at the Tevatron are well described by soft colour exchange models.
Their essence is the variation of colour string-field topologies giving both
gap and no-gap events, with a smooth transition and thereby a unified
description of all final states.Comment: 3 pages, 6 eps figures, contribution to the DIS 99 workshop
proceedings, uses npb.st

### Macroscopic proof of the Jarzynski-Wojcik fluctuation theorem for heat exchange

In a recent work, Jarzynski and Wojcik (2004 Phys. Rev. Lett. 92, 230602)
have shown by using the properties of Hamiltonian dynamics and a statistical
mechanical consideration that, through contact, heat exchange between two
systems initially prepared at different temperatures obeys a fluctuation
theorem. Here, another proof is presented, in which only macroscopic
thermodynamic quantities are employed. The detailed balance condition is found
to play an essential role. As a result, the theorem is found to hold under very
general conditions.Comment: 9 pages, 0 figure

### 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

### The Information Geometry of the One-Dimensional Potts Model

In various statistical-mechanical models the introduction of a metric onto
the space of parameters (e.g. the temperature variable, $\beta$, and the
external field variable, $h$, in the case of spin models) gives an alternative
perspective on the phase structure. For the one-dimensional Ising model the
scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in
the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) /
\sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. This is positive definite and, for
physical fields and temperatures, diverges only at the zero-temperature,
zero-field ``critical point'' of the model.
In this note we calculate ${\cal R}$ for the one-dimensional $q$-state Potts
model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B
(q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts
analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. This is no longer positive
definite, but once again it diverges only at the critical point in the space of
real parameters. We remark, however, that a naive analytic continuation to
complex field reveals a further divergence in the Ising and Potts curvatures at
the Lee-Yang edge.Comment: 9 pages + 4 eps figure

### Rigid rotators and diatomic molecules via Tsallis statistics

We obtain an analytic expression for the specific heat of a system of N rigid
rotators exactly in the high temperature limit, and via a pertubative approach
in the low temperature limit. We then evaluate the specific heat of a diatomic
gas with both translational and rotational degrees of freedom, and conclude
that there is a mixing between the translational and rotational degrees of
freedom in nonextensive statistics.Comment: 12 page

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