Fractional calculus as a macroscopic manifestation of randomness

Description:

Article discussing fractional calculus as a macroscopic manifestation of randomness.

Creator(s):
Creation Date: March 1999
Partner(s):
UNT College of Arts and Sciences
Collection(s):
UNT Scholarly Works
Usage:
Total Uses: 54
Past 30 days: 13
Yesterday: 1
Creator (Author):
Grigolini, Paolo

University of North Texas; Università di Pisa; Istituto di Biofisica

Creator (Author):
Rocco, A. (Andrea)

University of North Texas

Creator (Author):
West, Bruce J.

University of North Texas

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
Date(s):
  • Creation: March 1999
Description:

Article discussing fractional calculus as a macroscopic manifestation of randomness.

Degree:
Department: Physics
Note:

Copyright 1999 American Physical Review. The following article appeared in Physical Review E, 59:3, pp. 2603-2613; http://pre.aps.org/abstract/PRE/v59/i3/p2603_1

Note:

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.

Physical Description:

11 p.

Language(s):
Subject(s):
Keyword(s): fractional calculus | statistical mechanics
Source: Physical Review E, 1999, College Park: American Physical Society, pp. 2603-2613
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • DOI: 10.1103/PhysRevE.59.2603
  • ARK: ark:/67531/metadc77121
Resource Type: Article
Format: Text
Rights:
Access: Public
Citation:
Publication Title: Physical Review E
Volume: 59
Issue: 3
Page Start: 2603
Page End: 2613
Pages: 11
Peer Reviewed: Yes