Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Area of Science:

• Complex Fluids
• Statistical Mechanics
• Computational Physics

Background:

• Continuum hydrodynamic field equations are used for complex fluids, requiring noise for thermal fluctuations.
• Numerical discretisation schemes for these equations often include short-scale cutoffs.
• Active field theories introduce terms that break detailed balance, necessitating accurate entropy production rate calculations.

Purpose of the Study:

• To investigate the construction of numerical discretisation schemes for stochastic partial differential equations.
• To analyze the continuum limits of these schemes, focusing on models like 'Model B' for phase separation.
• To ensure steady-state entropy production rate (EPR) vanishes in equilibrium and is correctly calculated for active field theories.

Main Methods:

• Focus on purely diffusive scalar field models, specifically 'Model B'.
• Analysis of spurious drift and related terms dependent on discretisation schemes.
• Examination of both temporal and spatial discretisation effects on noise (additive vs. multiplicative).

Main Results:

• Subtleties in spurious drift arise from both temporal and spatial discretisation, even with additive noise.
• Noise can become multiplicative through off-diagonal couplings to additional fields.
• Careful accounting of spurious drift is crucial for accurate EPR evaluation and numerical implementation of Langevin dynamics.

Conclusions:

• Correctly calculating entropy production rates in active field theories depends critically on managing discretisation-induced spurious drift.
• The findings are applicable to various complex fluid models and active field theories.
• Accurate numerical implementation of Langevin dynamics requires careful treatment of these discretisation artifacts.