Anomalous relaxation in colloidal systems

The Mpemba effect refers to a phenomenon where a sample of hot water may cool and begin to freeze more quickly than a cool or warm water sample prepared under identical conditions. Although the effect has been known since the time of Aristotle, it is named after the Tanzanian teenager Erasto Mpemba, who discovered the effect in the 1960s. Although Mpemba and Osborne showed the effect in laboratory experiments, it has always been mysterious, its underlying mechanism a topic of hot debate. In this thesis, we experimentally show the Mpemba effect in a colloidal system with a micron-sized silica bead diffusing in a bath. The bead is subjected to an external double-well potential created by a feedback-based optical tweezer. When a system is quenched from an initially hot equilibrium state to a cold equilibrium state, the evolution of the system between the initial and the final state is a strongly nonequilibrium process. As a nonequilibrium state cannot, in general, be characterized by a single temperature, we adopt the notion of a "distance" measure as a proxy for temperature. We show Mpemba effects in an asymmetric double-well potential. Our experimental results agree quantitatively with predictions based on the Fokker-Planck equation. Using understanding gained from the Mpemba effect, we design an experiment to investigate the opposite effect and present the first experimental evidence for this inverse Mpemba effect. Contrary to the cooling effect, the inverse effect is related to a phenomenon where a system that is initially cold heats up faster than an initially warm system. By understanding the underlying mechanism of these anomalous effects, we demonstrate strong Mpemba and inverse Mpemba effects, where a system can cool or heat exponentially faster to the bath temperature than under typical conditions. Finally, we ask whether asymmetry in the potential is necessary and show experimentally that an anomalous cooling effect can be observed in a symmetric potential, leading to a higher-order Mpemba effect.