Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions
arXiv:cond-mat/0406120 · doi:10.1016/j.physa.2004.08.004
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.
30 pages
References in corpus (8)
- Dynamical foundations of nonextensive statistical mechanics
- Statistical Aging and Non Ergodicity in the Fluorescence of Single Nanocrystals
- Breakdown of the Onsager principle as a sign of aging
- Dynamics of Annealed Systems under External Fields: CTRW and the Fractional Fokker-Planck Equations
- Absorption and Emission in the non-Poisson case
- Strange kinetics: conflict between density and trajectory description
- Trajectory versus probability density entropy
- Decoherence, wave function collapses and non-ordinary statistical mechanics