Creator: Allegrini, Paolo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo & West, Bruce J.
Description: Paper discussing non-Poisson processes and regression to equilibrium versus equilibrium correlation functions. Abstract: We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To fit the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to the equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order functions, an unsettled problem, which has been addressed in the past by means of approximation yielding quite different physical effects.
Contributing Partner: UNT College of Arts and Sciences