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Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production.

Michael E Cates1, Étienne Fodor2, Tomer Markovich3

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Accurate simulation of active field theories requires careful handling of numerical discretisation. This study addresses spurious drift terms in spatial and temporal discretisation to correctly calculate entropy production rates in complex fluid models.

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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.