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Sergei Izvekov1

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This study revisits coarse-grained (CG) particle dynamics derivation from atomistic systems. It reveals non-unique CG equations of motion and provides methods for constructing thermodynamically consistent models from microscopic data.

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Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Multiscale Modeling

Background:

  • Deriving coarse-grained (CG) particle equations of motion from microscopic Hamiltonian dynamics is crucial for multiscale simulations.
  • Existing methods face challenges due to energy exchange between CG and intraparticle degrees of freedom.

Purpose of the Study:

  • To revisit and clarify the derivation of CG equations of motion from equilibrium atomistic dynamics.
  • To explore the non-uniqueness of projection operators and its impact on generalized Langevin equations (GLEs).
  • To provide a framework for constructing thermodynamically consistent CG models with momentum-dependent memory functions.

Main Methods:

  • Projection operator method and time-convolution equation.
  • Analysis of idempotence properties for projection operators along system trajectories.
  • Computation and analysis of projected forces and their correlation with CG particle momenta.

Main Results:

  • Demonstrated non-unique CG equations of motion in the form of nonlinear generalized Langevin equations (GLEs).
  • Showed that streaming terms in GLEs are conservative forces, with non-conservative forces expressed via thermodynamic averages.
  • Derived explicit forms for position- and momentum-dependent memory functions, including a momentum-quadratic memory function example.

Conclusions:

  • The derived expressions enable the construction of thermodynamically consistent CG models with momentum-dependent memory.
  • The framework facilitates computational schemes for parameter extraction for GLEs and related models from microscopic simulations.
  • This work offers a rigorous foundation for developing accurate and efficient multiscale simulation methods.