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Dynamics of Fluctuations in Nonequilibrium Systems

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The main goal of the proposed project is to further develop the theory of nonequilibrium processes capitalizing on recent and planned progress in this field. In particular it is proposed to study the important role of long wave fluctuations and long-range correlations. The main thrust of the proposed studies is based on Bogolyubov's reduced description (RD) method. In the framework of this method a system is described by a set of parameters (RD parameters), which satisfy, closed Markovian equations (RD equations). The reduced description is designed to hold for sufficiently large time and it is based on a functional hypothesis, which expresses the statistical operator of the system through RD parameters. The power of the aforementioned method is in its ability to obtain reduced equations suitable for the study of both equilibrium and nonequilibrium correlations.
Most of the alternatives to the RD method in nonequilibrium statistical mechanics are usually based on reversible master equations whose long time limits can be irreversible. These limiting procedures are not universal and often inexact and they do not allow for a systematic study of correlations and the derivation of proper reduced descriptions.
Our teams have recently performed detailed studies of long-range nonequilibrium fluctuations in fluids and gases employing the RD method and its variants. In these investigations it has been shown that the concept of microscopically (length) smoothed kinetic and hydrodynamic fluctuations is very useful. New possibilities were opened by recently derived projection formulation of the RD method and introduction of a smoothing projection operator. In addition a novel master operator has proven instrumental in the study of the dynamics of correlations and the derivation of RD's.
It is presently common to revisit the existing results concerning the influence of fluctuations on nonequilibrium processes. Clearly it is important to study the connections among different approaches to nonequilibrium problems in order to better establish the validity of the results and observe universal features whenever possible. The comparison of new venues and old ones can be used to asses the limitations of each and come up with more general and useful results. It is for this very general reason that the derivation of RD's is to be put in the perspective offered by other alternatives.

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Tel Aviv University
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Klausner
69978 Tel Aviv
Israel

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Letzte Aktualisierung: 30 Oktober 2002

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Permalink: https://cordis.europa.eu/project/id/INTAS-2000-00577/de

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