The district of southern California is divided into small cubic cells. Each cell is regarded as a vertex of a random graph, when earthquakes with any values of magnitude occur therein. Successive earthquakes define an edge and a loop. Then, the seismic data are analyzed from the viewpoint of an evolving random network. It is found that the distribution of… (More)
The problem of quantum state inference and the concept of quantum entanglement are studied using a non-additive measure in the form of Tsallis' entropy indexed by the positive parameter q. The maximum entropy principle associated with this entropy along with its thermodynamic interpretation are discussed in detail for the Einstein-Podolsky-Rosen pair of two… (More)
The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive entropies. This limits the range of the nonextensivity parameter q to (,) 0 1 so as to preserve the concavity of the… (More)
Discoveries of the scale-free and small-world features are reported on a network constructed from the seismic data. It is shown that the connectivity distribution decays as a power law, and the value of the degrees of separation, i.e., the characteristic path length or the diameter, between two earthquakes (as the vertices) chosen at random takes a small… (More)
The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy and a complete proof of the uniqueness theorem for the Tsallis entropy is presented. This improves the discussion of dos Santos.
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… (More)
— The Internet is a complex system, whose temporal behavior is highly nonstationary and exhibits sudden drastic changes regarded as main shocks or catastrophes. Here, analyzing a set of time series data of round-trip time measured in echo experiment with the Ping Command, the property of " aftershocks " (i.e., catastrophes of smaller scales) after a main… (More)
The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, β. 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… (More)
The concept of composability states that entropy of the total system composed of independent subsystems is a function of entropies of the subsystems. Here, the most general pseudoadditivity rule for composable entropy is derived based only on the existence of equilibrium.
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… (More)