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

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.