Measuring kinetic energy changes in the mesoscale with low acquisition rates

Abstract: We describe a new technique to estimate the mean square velocity of a Brownian particle from time series of the position of the particle sampled at frequencies several orders of magnitude smaller than the momentum relaxation frequency. We apply our technique to determine the mean square velocity of single optically trapped polystyrene microspheres immersed in water. The velocity is increased applying a noisy electric field that mimics a higher kinetic temperature. Therefore, we are able to measure the average kinetic energy change in isothermal and non-isothermal quasistatic processes. Moreover, we show that the dependence of the mean square time-averaged velocity on the sampling frequency can be used to quantify properties of the electrophoretic mobility of a charged colloid. Our method could be applied to detect temperature gradients in inhomogeneous media and to characterize the complete thermodynamics of microscopic heat engines.