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Continuum balances from extended Hamiltonian dynamics.

Giulio G Giusteri1, Paolo Podio-Guidugli2, Eliot Fried1

  • 1Mathematical Soft Matter Unit, Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna, Okinawa 904-0495, Japan.

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Summary
This summary is machine-generated.

This study extends the Irving-Kirkwood-Noll procedure to extended Hamiltonian systems, yielding continuum balance equations with non-standard terms. Understanding these terms is crucial for multiscale computational schemes in molecular dynamics.

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Area of Science:

  • * Continuum Mechanics
  • * Statistical Mechanics
  • * Computational Physics

Background:

  • * Classical continuum mechanics balance laws are derived from Hamiltonian dynamics.
  • * Modern molecular dynamics simulations utilize extended Hamiltonians (e.g., Andersen, Nosé, Parrinello-Rahman) for enhanced statistical properties.
  • * Existing methods do not fully address the implications of these extended Hamiltonians within continuum frameworks.

Purpose of the Study:

  • * To develop a physically consistent application of the Irving-Kirkwood-Noll procedure for extended Hamiltonian systems.
  • * To derive continuum-level balance equations that incorporate auxiliary degrees of freedom from extended Hamiltonians.
  • * To identify and characterize the non-standard terms arising from these auxiliary degrees of freedom.

Main Methods:

  • * Application of the Irving-Kirkwood-Noll procedure to systems described by extended Hamiltonians.
  • * Derivation of continuum balance equations from atomistic descriptions with auxiliary variables.
  • * Analysis of the impact of additional fluxes and sources on thermodynamic and transport properties.

Main Results:

  • * Successful derivation of continuum balance equations for extended Hamiltonian systems.
  • * Identification of non-standard terms in the balance equations due to auxiliary degrees of freedom.
  • * Demonstration that these non-standard terms influence thermodynamic and transport properties.

Conclusions:

  • * The proposed method provides a consistent framework for bridging atomistic simulations with extended Hamiltonians to continuum models.
  • * The identified non-standard terms are essential for accurately capturing the behavior of systems simulated with extended Hamiltonians.
  • * Awareness of these additional contributions is critical for the development of accurate multiscale computational schemes.