Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions

Paolo Allegrini, Paolo Grigolini, Luigi Palatella, Angelo Rosa and Bruce J. West

Physica A: Statistical Mechanics and its Applications, 2005, vol. 347, issue C, 268-288

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 accomodate 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 the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.

Keywords: Stochastic processes; Non-Poisson processes; Liouville and Liouville-like equations; Correlation function; Regression to equilibrium (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:347:y:2005:i:c:p:268-288

DOI: 10.1016/j.physa.2004.08.004

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