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Equilibrium distribution functions: connection with microscopic dynamics.

Charlotte F Petersen1, Debra J Searles1,2

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This study presents a direct method to derive the equilibrium distribution function from microscopic dynamics. It clarifies when modified molecular dynamics simulations achieve equilibrium, particularly for driven charged particles and thermostatting methods.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Physical Chemistry

Background:

  • Standard derivations of the equilibrium distribution function use assumptions that may not be universally applicable.
  • Molecular dynamics (MD) simulations often modify equations of motion to explore different ensembles or phenomena.

Purpose of the Study:

  • To present a straightforward method for deriving the equilibrium distribution function from microscopic dynamics.
  • To analyze the conditions under which modified MD simulations sample equilibrium ensembles.
  • To investigate the validity of equilibrium sampling for specific simulation protocols.

Main Methods:

  • Derivation of the equilibrium distribution function directly from microscopic dynamics.
  • Analysis of modified equations of motion in MD simulations.
  • Examination of systems with charged particles driven by an external field.
  • Evaluation of SLLOD shear flow dynamics and Berendsen thermostat dynamics.

Main Results:

  • A straightforward approach to derive the equilibrium distribution function from microscopic dynamics is presented.
  • Modified MD equations of motion do not always sample equilibrium ensembles.
  • For charged particles driven by a field, equilibrium is achieved only in confined systems.
  • SLLOD shear flow and Berendsen thermostat dynamics do not sample time-independent phase space distributions.

Conclusions:

  • The presented method provides a rigorous way to obtain equilibrium distribution functions.
  • Understanding the conditions for equilibrium sampling is crucial for accurate MD simulations.
  • Specific simulation protocols, like driven charged particles in unconfined systems or certain thermostatting methods, may not yield equilibrium results.