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Sumiyoshi Abe

Publications and source records attributed to Sumiyoshi Abe.

At least 73 records · Page 4Linked to original sources
arXiv2010

Universal and nonuniversal distant regional correlations in seismicity: Random-matrix approach

Distant regional cross correlations are analyzed for seismicity in Japan by making use of the theory of random matrices as the null hypothesis. The empirical correlation matrix is shown to strongly deviate from the random matrix of the Wishart type. Accordingly, nonuniversal (i.e., nonrandom) correlations are identified and are represented by the networks on the map of Japan. The effect of setting threshold for magnitude is also examined, and it is found that the threshodling alters the results only slightly.

physics.geo-ph↗
arXiv2009

Anomalous behavior of q-averages in nonextensive statistical mechanics

A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific deformations of probability distributions. Here, the following three issues are discussed and clarified. Firstly, the deformations considered are physical and may experimentally be realized. Secondly, in view of thermostatistics, the q-average is unstable in both finite and infinite discrete systems. Thirdly, a naive generalization of the discussion to continuous systems misses a point, and a norm better than the $L^1$-norm should be employed for measuring the distance between two probability distributions. Consequently, stability of the q-average is shown not to be established in all the cases.

cond-mat.stat-mech↗
arXiv2009

Determination of the scale of coarse graining in earthquake network

In a recent paper [S. Abe and N. Suzuki, Europhys. Lett., 65 (2004) 581], the concept of earthquake network has been introduced in order to describe complexity of seismicity. There, the cell size, which is the scale of coarse graining needed for constructing an earthquake network, has remained as a free parameter. Here, a method is presented for determining it based on the scaling behavior of the network. Quite remarkably, both the exponent of the power-law connectivity distribution and the clustering coefficient are found to approach the respective universal values and remain invariant as the cell size becomes larger than a certain value, $l_*$, which depends on the number of events contained in the analysis, in general. This $l_*$ fixes the scale of coarse graining. Universality of the result is demonstrated for all of the networks constructed from the data independently taken from California, Japan and Iran.

physics.geo-ph↗
arXiv2009

Statistical quantum operation

A generic unital positive operator-valued measure (POVM), which transforms a given stationary pure state to an arbitrary statistical state with perfect decoherence, is presented. This allows one to operationally realize thermalization as a special case. The loss of information due to randomness generated by the operation is discussed by evaluating the entropy. Thermalization of the bipartite spin-1/2 system is discussed as an illustrative example.

cond-mat.stat-mech↗
arXiv2009

Generalized molecular chaos hypothesis and H-theorem: Problem of constraints and amendment of nonextensive statistical mechanics

Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated H-theorem, whereas the q-average widely used in the relevant literature is not. In the course of the analysis, the distributions with finite cut-off factors are rigorously treated. Accordingly, the formulation of nonextensive statistical mechanics is amended based on the normal average. In addition, the Shore-Johnson theorem, which supports the use of the q-average, is carefully reexamined, and it is found that one of the axioms may not be appropriate for systems to be treated within the framework of nonextensive statistical mechanics.

cond-mat.stat-mech↗
arXiv2008

Violation of the scaling relation and non-Markovian nature of earthquake aftershocks

The statistical properties of earthquake aftershocks are studied. The scaling relation for the exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence of aftershocks is a singular Markovian process, is carefully examined. Data analysis shows significant violation of the scaling relation, implying the non-Markovian nature of aftershocks.

physics.geo-ph↗
arXiv2008

Instability of q-expectation value

q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. Here, it is shown that the q-expectation value is not stable under small deformations of a probability distribution function, in general, whereas the ordinary expectation value is always stable.

cond-mat.stat-mech↗
arXiv2008

Scaling relation for earthquake networks

The scaling relation derived by Dorogovtsev, Goltsev, Mendes and Samukhin [Phys. Rev. E, 68 (2003) 046109] states that the exponents of the power-law connectivity distribution, gamma, and the power-law eigenvalue distribution of the adjacency matrix, delta, of a locally treelike scale-free network satisfy 2*gamma - delta = 1 in the mean field approximation. Here, it is shown that this relation holds well for the reduced simple earthquake networks (without tadpole-loops and multiple edges) constructed from the seismic data taken from California and Japan. The result is interpreted from the viewpoint of the hierarchical organization of the earthquake networks.

physics.geo-ph↗
arXiv2008

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.

cond-mat.stat-mech↗
arXiv2008

Fluctuation theorem for the renormalized entropy change in the strongly nonlinear nonequilibrium regime

Generalizing a recent work [T. Taniguchi and E. G. D. Cohen, J. Stat. Phys. 126, 1 (2006)] that was based on the Onsager-Machlup theory, a nonlinear relaxation process is considered for a macroscopic thermodynamic quantity. It is found that the fluctuation theorem holds in the nonlinear nonequilibrium regime if the change of the entropy characterized by local equilibria is appropriately renormalized. The fluctuation theorem for the ordinary entropy change is recovered in the linear near-equilibrium case. This result suggests a possibility that the the information-theoretic entropy of the Shannon form may be modified in the strongly nonlinear nonequilibrium regime.

cond-mat.stat-mech↗
arXiv2007

Stationary photon-atom entanglement and flow equation

Stationary photon-atom entanglement is discussed by applying the method of flow equation to the Jaynes-Cummings model. A nonlocal continuous unitary transformation is explicitly constructed and the associated positive operator-valued measures for the photons and atom are obtained. Then, flow of the entanglement entropy is analyzed. A comment is also made on implementing the unitary operation in the method of flow equation. This method may offer a new strategy for quantum-state engineering.

quant-ph↗
arXiv2007

Superstatistics, thermodynamics, and fluctuations

A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary thermodynamics is recovered as a special case of the present theory, and corrections to it can be systematically evaluated. A generalization of Einstein's relation for fluctuations is presented using a maximum entropy condition.

cond-mat.stat-mech↗
arXiv2006

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.

physics.geo-ph↗
arXiv2006

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 $1/|1-q|$ . The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.

cond-mat.stat-mech↗
arXiv2006

Complex earthquake networks: Hierarchical organization and assortative mixing

To characterize the dynamical features of seismicity as a complex phenomenon, the seismic data is 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.

cond-mat.dis-nn↗
arXiv2006

Hierarchical and mixing properties of static complex networks emerging from the fluctuating classical random graphs

The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

cond-mat.stat-mech↗