Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Non-equilibrium Thermodynamics

Background:

• The stress tensor is crucial for understanding fluid dynamics and material properties.
• Existing models often struggle to accurately describe non-equilibrium systems with interacting particles.

Purpose of the Study:

• To formulate an exact stress tensor for interacting Brownian particles.
• To derive a generalized stress tensor for Landau-Ginzburg theory in non-equilibrium conditions.
• To investigate the relationship between stress tensor, external potentials, and particle currents.

Main Methods:

• Stochastic equations for density operators.
• Derivation of exact and Landau-Ginzburg stress tensors.
• Analysis of spatio-temporal correlations and Green-Kubo relations.

Main Results:

• The derived stress tensor for Brownian particles matches previous results.
• Particle currents induce additional forces in out-of-equilibrium systems.
• A general stress tensor form was established, applicable to various energy functionals.
• Spatial correlations of the stress tensor decay as power laws in driven confined systems.

Conclusions:

• The study provides a unified framework for stress tensors in equilibrium and non-equilibrium systems.
• The findings are relevant for understanding phenomena like classical Casimir forces.
• The research clarifies the role of stress tensor components in transport coefficients such as viscosity.