General continuum approach for dissipative systems of repulsive particles

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Plasma Physics

Background:

• Dissipative systems with repulsive particles are common in physics.
• Understanding particle-particle correlations is crucial for modeling these systems.
• Existing models often struggle to incorporate these correlations effectively.

Purpose of the Study:

• To develop a general coarse-graining method for dissipative systems.
• To derive a continuity equation that accounts for particle-particle correlations.
• To establish a link between particle energy and generalized thermostatistics.

Main Methods:

• A novel coarse-graining approach was employed.
• Continuity equations were derived incorporating particle-particle correlations.
• Nonlinear diffusion equations were obtained to describe overdamped dynamics.
• The method was applied to systems with short-ranged power-law potentials.

Main Results:

• A general method to derive continuity equations for dissipative systems was established.
• Particle-particle correlations were successfully incorporated into energy balance.
• A nonlinear diffusion equation representing overdamped dynamics was obtained.
• A correspondence between particle energy and Tsallis generalized thermostatistics was revealed for specific potentials.

Conclusions:

• The proposed method provides a general framework for coarse-graining dissipative systems.
• The derived continuum descriptions offer insights into microdynamical behavior.
• The methodology is applicable to systems like superconducting vortices and complex plasmas.
• Consistency was validated through molecular dynamics simulations.