Fractional calculus as a macroscopic manifestation of randomness

Grigolini, P, Rocco, A and West, BJ (1999) Fractional calculus as a macroscopic manifestation of randomness Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 59. pp. 2603-2613.

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Abstract

We generalize the method of Van Hove [Physica (Amsterdam) 21, 517 (1955)] so as to deal with the case of nonordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of the Van Hove method imposes randomness upon Hamiltonian dynamics, the resulting statistical process is described using normal calculus techniques. On the other hand, in the case where there is no time-scale separation, this generalized version of Van Hove's method not only imposes randomness upon the microscopic dynamics, but it also transmits randomness to the macroscopic level. As a result, the correct description of macroscopic dynamics has to be expressed in terms of the fractional calculus.

Item Type:	Article
Divisions :	Surrey research (other units)
Authors :	Name Email ORCID Grigolini, P Rocco, A a.rocco@surrey.ac.uk West, BJ
Date :	March 1999
Depositing User :	Symplectic Elements
Date Deposited :	17 May 2017 09:40
Last Modified :	24 Jan 2020 17:26
URI:	http://epubs.surrey.ac.uk/id/eprint/824696

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