The framework of multifractal analysis (MFA) is distilled to the most sophisticated one. Within this transparent framework, it is shown that the harmonious representation of MFA utilizing two distinct Tsallis distribution functions, one for the tail part of probability density function (PDF) and...

We provide a unifying axiomatics for Rényi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszár's measure of directed divergence known from communication theory.

An analytical formula of the scaling exponents of velocity structure function for fully developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the Renyi entropy or the Havrda–Charvat–Tsallis...

An analytical formula for the probability density function (PDF) of the velocity fluctuation in fully-developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the Rényi entropy or the Tsallis...

In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for...

The general scaling theory of transient phenomena near the instability point, which has been proposed by one of the present authors (M.S.), is applied to investigate the fluctuation and relaxation of superradiance near the complete inversion (or instability point). An exact solution for a simple...

After reviewing the real-time formalism of dissipative quantum field theory, i.e. non-equilibrium thermo field dynamics (NETFD), a kinetic equation, a self-consistent equation for the dissipation coefficient and a “mass” or “chemical potential” renormalization equation for...

The solvable model of quantum-statistical mechanical frequency modulation, which was proposed previously by the authors, is solved exactly by rigorous treatment of the damping operator for the cases of boson and two-state irrelevant subsystems to obtain the intensity distribution and the...

The effects of the interaction between atoms and a laser field on the damping phenomena of the laser system are examined by the perturbational treatment of the rigorous damping theory. Correction terms to the conventional master equation of the laser system are obtained and those to the...

The transient behavior of laser radiation from the unstable state (i.e., no photon at the initial time) is treated by the WKB treatment proposed by Caroli et al., and comparison of the results with those of the scaling theory is given. A simple approximation, needed for the WKB treatment to...