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Microscopic derivation of particle-based coarse-grained dynamics: Exact expression for memory function.

Sergei Izvekov¹

¹Weapons and Materials Research Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, USA.

The Journal of Chemical Physics

|April 8, 2017

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New projection operators enable exact solutions for coarse-grained dynamics using generalized Langevin equations. This research offers computationally affordable expressions for molecular dynamics simulations.

Area of Science:

Statistical Mechanics
Computational Chemistry
Chemical Physics

Background:

Generalized Langevin equations (GLEs) are crucial for coarse-grained dynamics.
Traditional Mori-Zwanzig formalism with standard projection operators has limitations in exact solutions.
Recent advancements introduced new projection operators for exact coarse-grained dynamics.

Purpose of the Study:

To clarify the definition and application of new projection operators within the Mori-Zwanzig formalism.
To derive exact expressions for projected dynamics and the projected force.
To formulate a new exact formula for the memory function in coarse-grained systems.

Main Methods:

Utilizing a new family of projection operators within the Mori-Zwanzig formalism.

Related Experiment Videos

Calculating the projected dynamics exactly for a microscopic system in equilibrium.

Deriving the projected force as a "generalized additive fluctuating force".

Main Results:

An exact expression for the projected force was derived.
A new exact formula for the memory function was formulated, incorporating microscopic and coarse-grained forces.
Two important limiting cases (Markov limit and weak momentum dependence) were analyzed.

Conclusions:

The new formalism allows for exact solutions of projected dynamics.
Computationally affordable expressions for memory functions were developed.
These findings facilitate efficient evaluation from standard molecular dynamics simulations.