Volume 140, Number 6, December 2022
|Number of page(s)||7|
|Section||Mathematical and interdisciplinary physics|
|Published online||28 December 2022|
On the derivation of the generalized Langevin equation and the fluctuation-dissipation theorem
Sorbonne Université, Institut des sciences du calcul et des données, ISCD - F-75005 Paris, France
(a) E-mail: firstname.lastname@example.org (corresponding author)
Received: 26 September 2022
Accepted: 14 December 2022
The generalized Langevin equation is widely used to model the effective dynamics of chemical, soft or biological systems. It is used to describe the evolution of a small number of collective variables, and is derived using the projection operator formalism. However, the validity of the derivation of the generalized Langevin equation in systems featuring non-linear potential of mean force is presently questioned. In this paper, we rigorously derive, using a two-projection operator formalism, the usual form of the generalized Langevin equation with non-linear potential of mean force and constant memory kernel. We show that the usual fluctuation-dissipation theorem is violated and a modified version should be considered. We also illustrate this violation on a numerical example.
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