Non-equilibrium (thermo)dynamics of colloids under mobile piston compression

Abstract

We investigate the non-equilibrium compression of a confined hard-sphere colloidal fluid driven by a mobile boundary within dynamical density functional theory. The system consists of a fluid confined between two parallel walls, one acting as an overdamped piston subjected to a sudden increase in external pressure. The piston motion is controlled by a mobility parameter $K$, which sets the relative timescale between mechanical driving and diffusive relaxation. By varying $K$ over several orders of magnitude, we identify a crossover from quasi-static compression to a diffusion-limited strongly driven regime. For small $K$, the system evolves close to equilibrium and the total injected work approaches the equilibrium free-energy difference. For large $K$, the piston rapidly adjusts and the dynamics becomes governed by diffusive relaxation, leading to saturation in the piston trajectory, pressure--position relation, particle currents, and center-of-mass velocity. In this regime, the injected work and entropy production are bounded, reflecting constraints imposed by diffusive transport. The maximum injected power scales linearly with $K$, while the entropy-production peak exhibits a crossover from quadratic growth to saturation, with peak times displaying $1/K$ scaling. The entropy change of the thermal bath interpolates between a reversible limit and a strongly driven dissipative regime. Finally, the evolution of configurational entropy and external potential energy reveals a dynamical decoupling between confinement and structural relaxation, including transient non-monotonic behavior. These results provide a quantitative thermodynamic characterization of boundary-driven compression.

17 pages, 10 figures

References in corpus (32)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Active Particles in Complex and Crowded Environments
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Steady State Thermodynamics of Langevin Systems
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• Turning bacteria suspensions into a "superfluid"
• Classical dynamical density functional theory: from fundamentals to applications
• Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Power functional theory for Brownian dynamics
• Distribution of Entropy Production for a Colloidal Particle in a Nonequilibrium Steady State
• Coarse-Grained Modelling Out of Equilibrium
• Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps
• Power functional theory for many-body dynamics
• A dynamic density functional theory for particles in a flowing solvent
• Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
• General Non-equilibrium Theory of Colloid Dynamics
• Density profiles of a colloidal liquid at a wall under shear flow
• Mean-field dynamical density functional theory
• Mesoscopic virial equation for nonequilibrium statistical mechanics
• Extended dynamical density functional theory for colloidal mixtures with temperature gradients
• Flow and structure in nonequilibrium Brownian many-body systems
• Structural nonequilibrium forces in driven colloidal systems
• Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining
• Perspective: New directions in dynamical density functional theory
• Non-equilibrium dynamics of a confined colloidal bilayer in planar shear flow
• The Simplest Piston Problem I: Elastic Collisions
• Dissipative collapse of the adiabatic piston
• Memory effects in colloidal motion under confinement and driving