Contracted description of fluctuating systems

B.U. Felderhof and R.B. Jones

Physica A: Statistical Mechanics and its Applications, 1980, vol. 102, issue 1, 179-192

Abstract: We consider thermal fluctuations in a system with many degrees of freedom described by macroscopic equations and discuss the question how by elimination of variables one can arrive at a contracted stochastic equation for a subsystem. It is shown that for the validity of the fluctuation-dissipation theorem in the contracted description it is necessary to formulate the linear macroscopic equations in such a way that the equal-time thermal fluctuations of the subsystem are statistically independent of the variables which are eliminated. If this is not the case then a preliminary transformation of variables is required. As special cases we discuss the derivation of the Langevin equation for a Brownian particle immersed in a fluid and for a particle embedded in a harmonic lattice.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:102:y:1980:i:1:p:179-192

DOI: 10.1016/0378-4371(80)90068-0

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