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...

In this paper, we quantify the statistical coherence between financial time series by means of the Rényi entropy. With the help of Campbell’s coding theorem, we show that the Rényi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly...

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the...

In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of Rényi’s entropy and the mean squared error analysis to...

Within the formalism of non-equilibrium thermo field dynamics (NETFD), a derivation of basic equations is given in their most general and suitable forms to take into account the coarse graining in the kinetic region and in the fluid mechanical region. A new concept, called the connection of...

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...

Degenerate parametric amplification accompanied by dissipation is analyzed within the canonical operator formalism for quantum dissipative systems named non-equilibrium thermo field dynamics. The vacuum of the system is subject to both dissipation and breaking of phase symmetry due to squeezing....

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...