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...

The concept of work is studied in quantum thermodynamics of a system surrounded by an environment and driven by a slowly varying external force. It is found that there appears the gauge theoretical structure in a nonequilibrium quasistationary state generated from the equilibrium state through a...

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...

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...

Nonextensive statistical mechanics based on the maximum Tsallis entropy principle and its physical backgrounds are summarized. The Boltzmann equation with a generalized form of Stosszahlansatz and the associated H-theorem are proposed and analyzed in order to examine if relaxation of a...

The statistical property of the calm times, i.e., time intervals between successive earthquakes with arbitrary values of magnitude, is studied by analyzing the seismic time series data in California and Japan. It is found that the calm times obey the Zipf–Mandelbrot power law, exhibiting a new...

Composability of entropy implies that entropy of the total system composed of independent subsystems is given by a function of entropies of the subsystems. It is shown that the zeroth law of thermodynamics naturally leads to Tsallis-type pseudoadditivity of the composable entropies. Then,...

An earthquake network is known to be of the small-world type. The values of the network’s characteristics, however, depend not only on the cell size (i.e., the scale of coarse graining needed for constructing the network) but also on the size of a seismic data set. Here, discovery of a scaling...

Gibbs’ theorem valid for systems with the extensive entropy is generalized for systems possessing nonextensive entropies, and macroscopic thermodynamics of equilibrium is established for systems obeying the power-law distributions.