Quantitative analysis of non-equilibrium systems from short-time experimental data

Estimating entropy production directly from experimental trajectories is of great current interest but often requires a large amount of data or knowledge of the underlying dynamics. In this paper, we propose a minimal strategy using the short-time Thermodynamic Uncertainty Relation (TUR) by means of which we can simultaneously and quantitatively infer the thermodynamic force field acting on the system and the (potentially exact) rate of entropy production from experimental short-time trajectory data. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, prior to studying the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. In the latter case, we build an effective model of the system based on our results. In both cases, we also demonstrate that our results match with those obtained from another recently introduced scheme. Thermal fluctuations play a crucial role in non-equilibrium phenomena at microscopic length scales, making it challenging to analyse and interpret experimental data. Here, the authors demonstrate that the short-time thermodynamic uncertainty relation inference scheme can estimate the entropy production rate for a colloidal particle in time-varying potentials and with background flows determined by the presence of a microbubble.