Comparison of some master equation descriptions of relaxation in complex systems

A.K. Rajagopal, K.L. Ngai, R.W. Rendell and S. Teitler

Physica A: Statistical Mechanics and its Applications, 1988, vol. 149, issue 1, 358-368

Abstract: Several models of relaxation based on master equation approaches have obtained the Kohlrausch fractional exponential form φ(t) = exp − (tτ∗)1−n, 0 < n < 1, or its equivalent for the relaxation function in complex systems. Representative models include (i) the Cohen-Grest free-volume theory, (ii) the work of Dhar and Barma, and Skinner based on Glauber's kinetic Ising model, (iii) the theory of De Dominicis et al. based on a random energy model for the spin glass, (iv) the Ogielski-Stein theory based on dynamics in an ultrametric space, and (v) Ngai's theory of time-dependent transition rates. In view of the different nature of these models and because of the claims that they are applicable outside of their original contexts, it is useful to make an intercomparison of these models and their consequences. A presentation of these models is here given based on a unified master equation approach. By experiment, many real systems have been shown to exhibit not only the Kohlrausch form but two additional related properties which are not encompassed in model types (i)–(iv). Only models that include time-dependent transition rates have so far been shown to be consistent with the experimental observations of the three empirical relations.

Date: 1988
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437188902257
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:149:y:1988:i:1:p:358-368

DOI: 10.1016/0378-4371(88)90225-7

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().