28,155 research outputs found
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
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
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
Justification of Power-Law Canonical Distributions Based on Generalized Central Limit Theorem
A self-consistent thermodynamic framework is presented for power-law
canonical distributions based on the generalized central limit theorem by
extending the discussion given by Khinchin for deriving Gibbsian canonical
ensemble theory. The thermodynamic Legendre transform structure is invoked in
establishing its connection to nonextensive statistical mechanics.Comment: 8 pages. Some minor corrections are made, with no changes in the
conclusion
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
Support Vector Machines in Analysis of Top Quark Production
Multivariate data analysis techniques have the potential to improve physics
analyses in many ways. The common classification problem of signal/background
discrimination is one example. The Support Vector Machine learning algorithm is
a relatively new way to solve pattern recognition problems and has several
advantages over methods such as neural networks. The SVM approach is described
and compared to a conventional analysis for the case of identifying top quark
signal events in the dilepton decay channel amidst a large number of background
events.Comment: 8 pages, 8 figures, to be published in the proceedings of the
"Advanced Statistical Techniques in Particle Physics" conference in Durham,
UK (March, 2002
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