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Sumiyoshi Abe

Publications and source records attributed to Sumiyoshi Abe.

13 recordsLinked to original sources
PubMed2006

Temporal extensivity of Tsallis' entropy and the bound on entropy production rate.

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis entropy indexed by q is temporally extensive: linear growth in time, i.e., finite entropy production rate. Then, the universal bound on the entropy production rate is shown to be 1/ absolute value (1-q). The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.

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PubMed2006

Complex earthquake networks: hierarchical organization and assortative mixing.

To characterize the dynamical features of seismicity as a complex phenomenon, the seismic data are mapped to a growing random graph, which is a small-world scale-free network. Here, hierarchical and mixing properties of such a network are studied. The clustering coefficient is found to exhibit asymptotic power-law decay with respect to connectivity, showing hierarchical organization. This structure is supported by not only main shocks but also small shocks, and may have its origin in the combined effect of vertex fitness and deactivation by stress release at faults. The nearest-neighbor average connectivity and the Pearson correlation coefficient are also calculated. It is found that the earthquake network has assortative mixing. This is a main difference of the earthquake network from the Internet with disassortative mixing. Physical implications of these results are discussed.

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PubMed2005

Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution.

In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from fluctuating Erdös-Rényi random graphs. Using a quantum-mechanical method, the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations and generates a generic degree distribution through the Poisson transformation. As an example, a static scale-free network is discussed and the corresponding hidden variable distribution is found to decay as a power law and to diverge at the origin.

Algorithms↗
PubMed2005

Origin of the usefulness of the natural-time representation of complex time series.

The concept of natural time turned out to be useful in revealing dynamical features behind complex time series including electrocardiograms, ionic current fluctuations of membrane channels, seismic electric signals, and seismic event correlation. However, the origin of this empirical usefulness is yet to be clarified. Here, it is shown that this time domain is in fact optimal for enhancing the signals in time-frequency space by employing the Wigner function and measuring its localization property.

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PubMed2005

Necessity of q-expectation value in nonextensive statistical mechanics.

In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation value of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort distribution. Since both of them lead to the maximum-Tsallis-entropy distributions of a similar type, it is of crucial importance to determine which the correct physical one is. A point is that the definition of expectation value is indivisibly connected to the form of generalized relative entropy. Studying the properties of the relative entropies associated with these two definitions, it is shown how the use of the escort distribution is essential. In particular, the Shore-Johnson theorem for consistent minimum cross-entropy (i.e., relative-entropy) principle is found to select the formalism with the normalized q-expectation value and to exclude the possibility of using the ordinary expectation value from nonextensive statistical mechanics.

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PubMed2004

Aging in coherent noise models and natural time.

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the q-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.

Aging↗
PubMed2004

Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion.

Based on the canonical formalism, the dilatation symmetry is implemented to the Fokker-Planck equation for the Wigner distribution that describes atomic motion in an optical lattice. This reveals the symmetry principle underlying the recent result obtained by Lutz [Phys. Rev. A 67, 051402(R) (2003)] on the connection between anomalous transport in the optical lattice and Tsallis statistics in the high-energy regime. A condition is derived for the general linear Fokker-Planck equation to admit a nonstationary solution distribution that decays as a power law.

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PubMed2003

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 q in (0, 2]. 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.

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PubMed2003

Geometry of escort distributions.

Given an original distribution, its statistical and probabilistic attributes may be scanned using the associated escort distribution introduced by Beck and Schlögl 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 Cramér-Rao inequality leads to a fundamental limit for the precision of the statistical estimate of the order of the escort distribution. We also show quantitatively that it is inappropriate to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics.

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PubMed2003

Itineration of the Internet over nonequilibrium stationary states in Tsallis statistics.

The cumulative probability distribution of sparseness time interval in the Internet is studied by the method of data analysis. Round-trip time between a local host and a destination host through ten odd routers is measured using the ping command, i.e., doing an echo experiment. The data are found to be well described by q-exponential distributions, which maximize the Tsallis entropy indexed by q less or larger than unity, showing a scale-invariant feature of the system. The network is observed to itinerate over a series of the nonequilibrium stationary states characterized by Tsallis statistics.

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PubMed2002

Stability of Tsallis entropy and instabilities of Rényi 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 Rényi 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.

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