Earthquake network captures the complexity of seismicity in a peculiar manner. Given a seismic data, the procedure of constructing an earthquake network proposed by Abe and Suzuki (2004) contains as a single parameter the size of the cells, into which a geographical region under consideration is...

A part of the seismic time series, in which the Omori law for temporal pattern of aftershocks holds, is referred to as the Omori regime. Here the properties of correlation between earthquake events both inside and outside of the Omori regime are studied by analysis of the data taken in southern...

Macroscopic nonextensive thermodynamics is studied without recourse to microscopic statistical mechanics. Taking the Tsallis entropy as an example, it is shown that the concept of the physical temperature introduced through the generalized zeroth law of thermodynamics necessarily leads to...

Nonextensive quantum thermostatistics is shown to be consistent with the second law of thermodynamics if the entropic index, q, is in the range (0,2]. Clausius’ inequality is derived by making use of the convexity property of the quantum q-divergence which is a nonadditive generalization of...

Based on the form invariance of the structures given by Khinchin's axiomatic foundations of information theory and the pseudoadditivity of the Tsallis entropy indexed by q, the concept of conditional entropy is generalized to the case of nonadditive (nonextensive) composite systems. The proposed...

The statistical properties of earthquake aftershocks are studied. The scaling relation for 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...

Generalized quantum information theory is developed based on the nonadditive Tsallis entropy indexed by q. To see how this formalism is superior to the ordinary additive theory with the von Neumann entropy realized in the limit q→1, the problem of quantum entanglement of mixed states is...

The problem of the temperature in nonextensive statistical mechanics is studied. Considering the first law of thermodynamics and a “quasi-reversible process”, it is shown that the Tsallis entropy becomes the Clausius entropy if the inverse of the Lagrange multiplier, β, associated with the...

The temporal behavior of the Internet is studied by performing Ping experiments. Sudden drastic changes in the Internet time series of round-trip times of the Ping signals (i.e., congestion of the network) are catastrophic and can be identified as “Internetquakes”. Magnitude of the...

The quantum q-divergence is the nonadditive relative entropy associated with the Tsallis entropy indexed by q. Here, its basic properties including the q-deformation and quantum-group structure, convexity and monotonicity are summarized. Then, it is applied to measuring the degree of state...