Volume 136, Number 3, November 2021
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||23 February 2022|
The interplay between memory and potentials of mean force: A discussion on the structure of equations of motion for coarse-grained observables
Institute of Physics, University of Freiburg - Hermann-Herder-Str. 3, 79104 Freiburg, Germany
Received: 15 July 2021
Accepted: 2 November 2021
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can be obtained from the dynamics of the underlying microscopic system and in which cases it makes sense to introduce a potential of mean force. We discuss shortcomings of previous derivations presented in the literature and demonstrate the implications of our derivation for the structure of memory terms and for generalized fluctuation-dissipation relations. We show, in particular, that the widely used, simple structure which contains a potential of mean force, a memory term which is linear in the observable, and a fluctuating force which is related to the memory term by a fluctuation-dissipation relation, is neither exact nor can it, in general, be derived as a controlled approximation to the exact dynamics.
© 2022 The author(s)
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