Cooling dynamics of a Brownian particle and the Markovian Mpemba effect

I experimentally and numerically investigate a Mpemba-like behaviour in a colloidal particle diffusing in a bath under the influence of an externally applied potential. Multiple particle trajectories were recorded and used to obtain the spatial probability distribution of the particle at different times. As a temperature quench is applied, the probability distribution shifts from one equilibrium distribution to another that correspond to the initial and final temperatures in the process, respectively. I experimentally and numerically study the change in value of a measure for the degree of cooling calculated from the measured probability distributions that is compatible with the characteristics of temperature when the system is at equilibrium, and can equally be applied to a system that is out-of-equilibrium. I demonstrate that probability distributions can be estimated using a limited amount of data at sufficiently high accuracy to permit experimental observation of the Markovian Mpemba effect.