We present nonlinear stochastic differential equations, generating processes with the q-exponential and q-Gaussian distributions of the observables, i.e. with the long-range power-law autocorrelations and 1/fβ power spectral density. Similarly, the Tsallis q-distributions may be obtained in the...

In a previous paper [A. Carati, Physica A 348 (2005) 110–120] it was shown how, for a dynamical system, the probability distribution function of sojourn-times in phase-space, defined in terms of the dynamical orbits (up to a given observation time), induces unambiguously a statistical ensemble...

This paper is a natural continuation of a previous one by the author, which was concerned with the foundations of statistical thermodynamics far from equilibrium. One of the problems left open in that paper was the correct definition of temperature. In the literature, temperature is in general...

For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time averages, and the main problem then is how to formulate an appropriate statistical thermodynamics. The common answer is that the standard functional expression of Boltzmann–Gibbs for...

The statistics of the eigenvalues of symmetric random matrices, composed by real and statistically independent elements following the distribution that maximizes Tsallis's entropy, is carried numerically in the limit of large matrices. For entropic indexes in the interval −∞<q<53, by using a convenient rescale of variables, it is possible to show that such matrices fall in the same class of the Gaussian orthogonal ensemble (GOE). For the entropic index 53⩽q<3, the density of eigenvalues and the distribution of level spacings do not seem to follow a simple rescale of variables involving different values of q, and exhibit a behavior very distinct from the GOE: both quantities present long tails for 53⩽q⩽2, and such long tails die out when q>2. The density of...</q<53,>

We propose a model for cell migration where epithelial cells are able to detect trajectories of other cells and try to follow them. As cells move along in 2D cell culture, they mark their paths by loosing tiny parts of cytoplasm. Any cell moving on a surface where other cells have moved before...