All- and one-particle distribution functions at nonequilibrium steady state under thermal gradient

Area of Science:

• Statistical Mechanics
• Nonlinear Dynamics
• Computational Physics

Background:

• Non-equilibrium steady states (NESS) are crucial for understanding systems driven by external forces, such as heat conduction.
• Traditional methods often struggle to accurately describe the phase-space distribution function in NESS, particularly under thermal gradients.
• Molecular dynamics simulations are vital tools for investigating microscopic transport phenomena.

Purpose of the Study:

• To develop a concrete expression for the phase-space distribution function in a nonequilibrium steady state under a constant thermal gradient.
• To incorporate novel entropy production terms accounting for changes in equilibrium thermodynamic variables.
• To derive and validate Green-Kubo relations for one-particle distribution functions in NESS.

Main Methods:

• Formulation of the phase-space distribution function for all particles in a local volume.
• Inclusion of entropy production from changes in equilibrium thermodynamic variables.
• Derivation of Green-Kubo relations for density and velocity one-particle distribution functions.
• Verification using molecular dynamics simulations of a Lennard-Jones liquid.

Main Results:

• A tractable expression for the phase-space distribution function at nonequilibrium steady state under a thermal gradient.
• Successful derivation of Green-Kubo relations for one-particle distribution functions.
• Validation of the derived expressions through molecular dynamics simulations.
• Demonstration that the formulation correctly accounts for entropy production beyond spatial gradients.

Conclusions:

• The developed formulation provides a practical tool for analyzing nonequilibrium systems.
• The derived Green-Kubo relations enable analytical evaluation of nonequilibrium averages.
• This work advances the understanding of heat conduction and related phenomena in nonequilibrium molecular dynamics simulations.