21,996 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
Aftershocks in Modern Perspectives: Complex Earthquake Network, Aging, and Non-Markovianity
The phenomenon of aftershocks is studied in view of science of complexity. In
particular, three different concepts are examined: (i) the complex-network
representation of seismicity, (ii) the event-event correlations, and (iii) the
effects of long-range memory. Regarding (i), it is shown the clustering
coefficient of the complex earthquake network exhibits a peculiar behavior at
and after main shocks. Regarding (ii), it is found that aftershocks experience
aging, and the associated scaling holds. And regarding (iii), the scaling
relation to be satisfied by a class of singular Markovian processes is
violated, implying the existence of the long-range memory in processes of
aftershocks.Comment: 28 pages, 6 figures and 1 table. Acta Geophysica, in pres
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 thermodynamic relations
The generalized zeroth law of thermodynamics indicates that the physical
temperature in nonextensive statistical mechanics is different from the inverse
of the Lagrange multiplier, beta. This leads to modifications of some of
thermodynamic relations for nonextensive systems. Here, taking the first law of
thermodynamics and the Legendre transform structure as the basic premises, it
is found that Clausius definition of the thermodynamic entropy has to be
appropriately modified, and accordingly the thermodynamic relations proposed by
Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be
rectified. It is shown that the definition of specific heat and the equation of
state remain form invariant. As an application, the classical gas model is
reexamined and, in marked contrast with the previous result obtained by Abe
[Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical
temperature and the unphysical pressure, the specific heat and the equation of
state are found to be similar to those in ordinary extensive thermodynamics.Comment: 17 pages. The discussion about the Legendre transform structure is
modified and some additional comments are mad
Perspectives on Nuclear Structure and Scattering with the Ab Initio No-Core Shell Model
Nuclear structure and reaction theory are undergoing a major renaissance with
advances in many-body methods, strong interactions with greatly improved links
to Quantum Chromodynamics (QCD), the advent of high performance computing, and
improved computational algorithms. Predictive power, with well-quantified
uncertainty, is emerging from non-perturbative approaches along with the
potential for new discoveries such as predicting nuclear phenomena before they
are measured. We present an overview of some recent developments and discuss
challenges that lie ahead. Our focus is on explorations of alternative
truncation schemes in the harmonic oscillator basis, of which our
Japanese--United States collaborative work on the No-Core Monte-Carlo Shell
Model is an example. Collaborations with Professor Takaharu Otsuka and his
group have been instrumental in these developments.Comment: 8 pages, 5 figures, accepted for publication in Proceedings of
Perspectives of the Physics of Nuclear Structure, JPS Conference Proceedings,
Japan (to appear
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
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
Validity of the second law in nonextensive quantum thermodynamics
The second law of thermodynamics in nonextensive statistical mechanics is
discussed in the quantum regime. Making use of the convexity property of the
generalized relative entropy associated with the Tsallis entropy indexed by q,
Clausius' inequality is shown to hold in the range of q between zero and two.
This restriction on the range of the entropic index, q, is purely quantum
mechanical and there exists no upper bound of q for validity of the second law
in classical theory.Comment: 12 pages, no figure
Hidden gauge structure and derivation of microcanonical ensemble theory of bosons from quantum principles
Microcanonical ensemble theory of bosons is derived from quantum mechanics by
making use of a hidden gauge structure. The relative phase interaction
associated with this gauge structure, described by the Pegg-Barnett formalism,
is shown to lead to perfect decoherence in the thermodynamics limit and the
principle of equal a priori probability, simultaneously.Comment: 10 page
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