Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Abstract

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff -- which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing for simplicity on models with a purely diffusive scalar field, such as `Model B' which describes phase separation in binary fluid mixtures. We address the requirement that the steady state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for `active field theories' in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR) we must make a careful treatment of so-called `spurious drift' and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative, via off-diagonal couplings to additional fields that encode thermodynamically the underlying chemical processes responsible for activity. In this case the spurious drift terms need careful accounting, not just to evaluate correctly the EPR, but also to numerically implement the Langevin dynamics itself.

arXiv comment27 pages, 4 figures

References in corpus (36)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Self-motile colloidal particles: from directed propulsion to random walk
• Motility-Induced Phase Separation
• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• Meso-scale turbulence in living fluids
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• How far from equilibrium is active matter?
• A theory of regularity structures
• Fluid dynamics of bacterial turbulence
• Dissipation: The phase-space perspective
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Active matter
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Microscopic theory for the phase separation of self-propelled repulsive disks
• The statistical physics of active matter: from self-catalytic colloids to living cells
• Spontaneous symmetry breaking in active droplets provides a generic route to motility
• Irreversibility in active matter systems: Fluctuation theorem and mutual information
• Fluctuating lattice Boltzmann
• Theories of Binary Fluid Mixtures: From Phase-Separation Kinetics to Active Emulsions
• Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics
• Entropy production of active particles and for particles in active baths
• Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid
• Odd viscosity in active matter: microscopic origin and 3D effects
• Origins and diagnostics of the nonequilibrium character of active systems
• Capillary interfacial tension in active phase separation
• Rules of calculus in the path integral representation of white noise Langevin equations: the Onsager-Machlup approach
• Hydrodynamically interrupted droplet growth in scalar active matter
• Irreversibility in dynamical phases and transitions
• Critical Phenomena in Active Matter
• Critical active dynamics is captured by a colored-noise driven field theory
• Time-reversal symmetry violations and entropy production in field theories of polar active matter
• Shear-induced first-order transition in polar liquid crystals
• Systematic extension of the Cahn-Hilliard model for motility-induced phase separation
• Periodic patterns displace active phase separation

Cited by in corpus (21)

• Non-reciprocity across scales in active mixtures
• Variance Sum Rule for Entropy Production
• A review of active matter reviews
• Active phase separation: new phenomenology from non-equilibrium physics
• Entropons as collective excitations in active solids
• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Thermodynamics of active matter: Tracking dissipation across scales
• Entropy production and its large deviations in an active lattice gas
• Interface roughening in nonequilibrium phase-separated systems
• Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility
• Effective estimation of entropy production with lacking data
• Most probable path of an active Brownian particle
• Second Law of Thermodynamics without Einstein Relation
• Entropy production rate in thermodynamically consistent flocks
• Heat production in a stochastic system with nonlinear time-delayed feedback
• Most probable paths for active Ornstein-Uhlenbeck particles
• Entropy production in non-reciprocal polar active mixtures
• Entropy Production from Density Field Theories for interacting particles systems
• Effective Energy, Interactions And Out Of Equilibrium Nature Of Scalar Active Matter
• Intracellular phagosome shell is rigid enough to transfer outside torque to the inner spherical particle
• Consistent expansion of the Langevin propagator with application to entropy production