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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Statistical mechanical theory for non-equilibrium systems. IX. Stochastic molecular dynamics
1School of Chemistry F11, University of Sydney, New South Wales 2006, Australia. attard@chem.usyd.edu.au
The Journal of Chemical Physics
|May 27, 2009
Summary
This study presents a generalized fluctuation-dissipation theorem for nonequilibrium systems, establishing a molecular basis for friction. It reveals friction coefficients are proportional to the variance in stochastic equations of motion.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Computational Physics
Background:
- Understanding the behavior of non-equilibrium systems is crucial in various scientific fields.
- Existing models for friction in molecular dynamics often rely on continuum hydrodynamics, which may not be suitable at the molecular level.
- The fluctuation-dissipation theorem is a cornerstone of statistical mechanics, relating system fluctuations to dissipation.
Purpose of the Study:
- To derive a general form for probability density and transition probability in non-equilibrium systems.
- To establish a molecular foundation for Langevin's friction force, bypassing continuum hydrodynamics.
- To develop and test a stochastic molecular dynamics algorithm for both equilibrium and non-equilibrium scenarios.
Main Methods:
- Derivation of general probability density and transition probability for non-equilibrium systems.
- Maximization of transition probability to obtain a generalized fluctuation-dissipation theorem.
- Development of a stochastic molecular dynamics algorithm.
- Testing the algorithm with simulations of steady heat flow and driven Brownian particles.
Main Results:
- A generalized fluctuation-dissipation theorem is derived, providing a molecular basis for friction.
- The friction coefficient is shown to be directly proportional to the variance of the stochastic equations of motion.
- A novel stochastic molecular dynamics algorithm is successfully developed and validated.
Conclusions:
- The derived theorem offers a more fundamental understanding of friction in molecular systems.
- The proportionality between friction and variance is a key physical requirement identified.
- The developed algorithm is effective for simulating both equilibrium and non-equilibrium molecular dynamics problems.
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