Irreversible Boltzmann samplers in dense liquids: Weak-coupling approximation and mode-coupling theory.

Area of Science:

• Statistical Mechanics
• Non-equilibrium Dynamics
• Computational Physics

Background:

• Equilibrium statistical mechanics describes systems at thermal equilibrium.
• Langevin processes model particle dynamics influenced by random forces.
• Non-equilibrium systems exhibit complex dynamics not governed by Boltzmann statistics.

Purpose of the Study:

• To investigate the acceleration of Boltzmann steady-state sampling using transverse forces in a Langevin process.
• To quantify the impact of transverse forces on dynamical acceleration in a simple liquid.
• To analyze the relationship between transverse forces, transport coefficients, and temperature effects.

Main Methods:

• Simulating a simple liquid in three dimensions subjected to pairwise transverse forces.
• Analyzing the dynamics of a tracer particle in a weak coupling regime (high temperatures).
• Developing and applying a non-equilibrium mode-coupling theory to capture the effects of transverse forces.

Main Results:

• Transverse forces systematically accelerate the approach to the Boltzmann steady state.
• Dynamical acceleration correlates with increased odd transport coefficients (mobility, diffusivity).
• Acceleration decreases with increasing temperature beyond a crossover, particularly near the glass transition.

Conclusions:

• Transverse forces provide a minimal framework for accelerating Boltzmann sampling in Langevin dynamics.
• The developed non-equilibrium mode-coupling theory accurately predicts the observed acceleration.
• The findings offer insights into controlling and understanding non-equilibrium dynamics in physical systems.