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Position-dependent memory kernel in generalized Langevin equations: Theory and numerical estimation.

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|July 1, 2022
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Summary
This summary is machine-generated.

Generalized Langevin equations with non-linear forces and position-dependent friction are rigorously derived using the Mori-Zwanzig formalism. This work establishes a fluctuation-dissipation theorem and provides Volterra equations for model parametrization from simulations.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Physical Chemistry

Background:

  • Generalized Langevin equations model complex systems in molecular dynamics.
  • Non-linear forces and position-dependent friction kernels are crucial for accurate simulations.
  • The Mori-Zwanzig formalism provides a rigorous framework for deriving such equations.

Purpose of the Study:

  • To rigorously derive generalized Langevin equations with specific complexities.
  • To establish the relationship between noise and memory kernel via a fluctuation-dissipation theorem.
  • To develop a method for numerical parametrization of these models.

Main Methods:

  • Application of the Mori-Zwanzig formalism.
  • Derivation of generalized Langevin equations.
  • Analysis of fluctuation-dissipation relations.
  • Formulation of Volterra-type equations for memory kernels.

Main Results:

  • Rigorous derivation of generalized Langevin equations with non-linear forces and position-dependent friction kernels.
  • Demonstration of a fluctuation-dissipation theorem connecting noise properties to the memory kernel.
  • Obtained Volterra equations enabling numerical parametrization from all-atom simulations.

Conclusions:

  • The Mori-Zwanzig formalism successfully derives complex generalized Langevin equations.
  • A fundamental fluctuation-dissipation theorem is established for these systems.
  • The derived Volterra equations offer a practical approach for model parameterization in molecular dynamics.