Related papers: Universal relaxation function in nonextensive syst…
We derive a scaling property from a fundamental nonlinear differential equation whose solution is the so-called q-exponential function. A scaling property has been believed to be given by a power function only, but actually more general…
A novel theoretical expression for the relaxation time of magnetic nanoparticles with dipolar interactions is derived from Kramers' theory, extending the Boltzmann-Gibbs framework to incorporate Tsallis statistics. The model provides a…
It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the…
We analyse the rheological behaviour of the generalised Maxwell and Kelvin-Voigt models with a power law spectrum of relaxation or retardation times, ${\cal H}\sim 1/\tau^{\alpha}$ or ${\cal L}\sim \tau^\alpha$, respectively. When…
Carrying out explicitly the computation in a paradigmatic model of non-interacting systems, the Gaussian Model, we show the existence of a singular point in the probability distribution $P(M)$ of an extensive variable $M$. Interpreting…
We compute the probability of positive large deviations of the free energy per spin in mean-field Spin-Glass models. The probability vanishes in the thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the…
Recently, the complete left tail asymptotic for the density of the {\it martingale limit} of the classical Galton-Watson process has been derived. The derivation is based on the properties of a special function (whose inverse Fourier…
We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject…
Dielectric relaxation is universal in characterizing polar liquids and solids, insulators, and semiconductors, and the theoretical models are well developed. However, in high magnetic fields, previously unknown aspects of dielectric…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
In this paper we investigate a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order. In time domain these…
The role of macromolecular crowding in living systems is widely appreciated, but artificial crowders used to model these effects in vitro are often inadequately characterized. In this work, we examine density, viscosity, polymer…
The non-Debye, \textit{i.e.,} non-exponential, behavior characterizes a large plethora of dielectric relaxation phenomena. Attempts to find their theoretical explanation are dominated either by considerations rooted in the stochastic…
The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Levy process we study the nonlinear relaxation of the population density for…
In genuine nonequilibrium systems that undergo continuous driving, the thermodynamic forces are nonconservative, meaning they cannot be described by any free energy potential. Nonetheless, we show that the dynamics of such systems are…
We show how the interplay of non-linear dynamics, self-gravity, and fluctuations leads to self-affine behavior of matter density correlations quite generically, i.e., with a power-law exponent whose value does not depend in a very direct…
We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the…
Intermediate energy scale physics plays a very important role in non-equilibrium dynamics of quasi-low dimensional cold atom systems. In this article we obtain the universal scaling relations for the generalized reflection coefficient,…
We discuss the influence of white noise on a generic dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…