Aging and Rejuvenation with Fractional Derivatives Metadata
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- Main Title Aging and Rejuvenation with Fractional Derivatives
Author: Aquino, GerardoCreator Type: PersonalCreator Info: University of North Texas
Author: Bologna, MauroCreator Type: PersonalCreator Info: University of North Texas
Author: Grigolini, PaoloCreator Type: PersonalCreator Info: University of North Texas; Università di Pisa; Istituto dei Processi Chimico Fisici del Consiglio Nazionale delle Ricerche
Author: West, Bruce J.Creator Type: PersonalCreator Info: United States. Army Research Office
- Creation: 2008-02-02
- Physical Description: 11 p.: ill.
- Content Description: Article on aging and rejuvenation with fractional derivatives.
- Keyword: aging order
- Keyword: fractional derivatives
- Keyword: Onsager principle
- Keyword: fractional operators
- Website: arXiv: cond-mat/0311314
Name: UNT Scholarly WorksCode: UNTSW
Name: UNT College of Arts and SciencesCode: UNTCAS
- Rights Access: public
- Archival Resource Key: ark:/67531/metadc174699
- Academic Department: Physics
- Academic Department: Center for Nonlinear Science
- Display Note: This is the author manuscript version of an article published in Physical Review E.
- Display Note: Abstract: We discuss a dynamic procedure that makes the fractional derivative emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index μ in the interval 2 < μ < 3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord = μ - 2. If the system is prepared at time -tₐ < 0 and the observation begins at time t = 0, we derive the following scenario. For times 0 < t << tₐ the system is satisfactorily described by the fractional derivative with ord = 3 - μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t >> tₐ yields ord = μ - 2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.