Article
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On the Elimination of Fast Variables from the Langevin Equation
Version 1
: Received: 2 September 2024 / Approved: 2 September 2024 / Online: 3 September 2024 (03:36:23 CEST)
How to cite: Bedeaux, D. On the Elimination of Fast Variables from the Langevin Equation. Preprints 2024, 2024090099. https://doi.org/10.20944/preprints202409.0099.v1 Bedeaux, D. On the Elimination of Fast Variables from the Langevin Equation. Preprints 2024, 2024090099. https://doi.org/10.20944/preprints202409.0099.v1
Abstract
In a multivariable system there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux-force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables such that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.
Keywords
Langevin equation; fluctuation-dissipation theorems; fast and slow variables; Onsager symmetry relations; correlation functions
Subject
Physical Sciences, Thermodynamics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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