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Contracted description of fluctuating systems

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  • Felderhof, B.U.
  • Jones, R.B.

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.

Suggested Citation

  • Felderhof, B.U. & Jones, R.B., 1980. "Contracted description of fluctuating systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(1), pages 179-192.
    • Handle: RePEc:eee:phsmap:v:102:y:1980:i:1:p:179-192
    DOI: 10.1016/0378-4371(80)90068-0
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    References listed on IDEAS

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    1. Mazur, P. & van der Zwan, G., 1978. "Brownian motion in a fluid close to its' critical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(3), pages 483-500.
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