A state-based ergodic approach is introduced using a descriptor constructed from instantaneous, spatially resolved measurements to quantify the spatiotemporal evolution of system states in far-from-equilibrium systems. This method is demonstrated for the mixing process in confined water-glycerol flows driven across three milli-scale geometries, by combining experiments with lattice Boltzmann simulations that uniquely incorporate colloids as passive flow obstacles. This generalizable framework distinguishes nonequilibrium pathways by tracking information about accessed system states.

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• Nonequilibrium statistical mechanics
• Nonlinear dynamics in fluids
• Thermodynamics of mixing
• Nonequilibrium systems
• Ergodic theory
• Lattice-Boltzmann methods
• Phase space dynamics