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Fluctuation-induced forces occur generically when long-ranged correlations(e.g., in fluids) are confined by external bodies. In classical systems, suchcorrelations require specific conditions, e.g., a medium close to a criticalpoint. On the other hand, long-ranged correlations appear more commonly incertain non-equilibrium systems with conservation laws. Consequently, a varietyof non-equilibrium fluctuation phenomena, including fluctuation-induced forces,have been discovered and explored recently. Here, we address a long-standingproblem of non-equilibrium critical Casimir forces emerging after a quench tothe critical point in a confined fluid with order-parameter-conserving dynamicsand non-symmetry-breaking boundary conditions. The interplay of inherent(critical) fluctuations and dynamical non-local effects (due to densityconservation) gives rise to striking features, including correlation functionsand forces exhibiting oscillatory time-dependences. Complex transient regimesarise, depending on initial conditions and the geometry of the confinement. Ourfindings pave the way for exploring a wealth of non-equilibrium processes incritical fluids (e.g., fluctuation-mediated self-assembly or aggregation). Incertain regimes, our results are applicable to active matter.

Dynamics of the critical Casimir force for a conserved order parameter after a critical quench