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Related Experiment Videos

An idealized model for nonequilibrium dynamics in molecular systems.

Marc Vogt1, Rigoberto Hernandez

  • 1Center for Computational and Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA.

The Journal of Chemical Physics
|October 22, 2005
PubMed
Summary

The irreversible generalized Langevin equation (iGLE) models complex chemical dynamics. This study shows its underlying mechanical system is numerically solvable, enabling new studies of nonequilibrium systems.

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Area of Science:

  • Chemical Dynamics
  • Statistical Mechanics
  • Nonlinear Systems

Background:

  • Nonequilibrium dynamics in nonlinear systems exhibit emergent chemical behavior.
  • Stationary projected stochastic representations like the Langevin equation (LE) and generalized Langevin equation (GLE) cannot fully capture this behavior.
  • The irreversible generalized Langevin equation (iGLE) features a nonstationary friction kernel, reducing to GLE in specific limits.

Purpose of the Study:

  • To demonstrate the numerical solvability of the open Hamiltonian system corresponding to the iGLE.
  • To validate the iGLE by comparing simulations of the Hamiltonian system with its projected form.
  • To establish the utility of this extended Hamiltonian for studying nonequilibrium phenomena.

Main Methods:

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  • Numerical integration of an open Hamiltonian system with a nonlocal term.
  • Simulations of the mechanical system to analyze energy and solvent force correlations.
  • Comparison of simulation results with the projected irreversible generalized Langevin equation.

    • Main Results:

    • The open Hamiltonian system associated with the iGLE is amenable to numerical integration.
    • Simulations confirm precise agreement between the time-dependent total energy and solvent force correlations of the mechanical system and the projected iGLE.
    • The extended nonstationary Hamiltonian accurately reflects the dynamics described by the iGLE.

    Conclusions:

    • The developed numerical approach allows for the study of systems described by the iGLE.
    • This work bridges the gap between theoretical models and computational simulations for complex chemical dynamics.
    • The findings facilitate the investigation of nonequilibrium bounds and fluctuation theorems in nonlinear systems.