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.

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A large number of processes in the mesoscopic world occur out of equilibrium, where the time course of the system evolution becomes immensely important -they being driven principally by dissipative effects. Non-equilibrium steady states (NESS) represent a crucial category in such systems -which are widely observed in biological domains -especially in chemical kinetics in cellular processes [1], and molecular motors [2]. In this study, we employ a model NESS stochastic system which comprises of an colloidal microparticle, optically trapped in a viscous fluid and externally driven by a temporally correlated colored noise, and show that the work done on the system and the work dissipated by it -both follow the three Lévy arcsine laws. These statistics remain unchanged even in the presence of a perturbation generated by a microbubble at close proximity to the trapped particle. We confirm our experimental findings with theoretical simulations of the systems. Our work provides an interesting insight into the NESS statistics of the meso-regime, where stochastic fluctuations play a pivotal role.

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We provide a minimal strategy for the quantitative analysis of a large class of non-equilibrium systems in a steady state using the short-time Thermodynamic Uncertainty Relation (TUR). From short-time trajectory data obtained from experiments, we demonstrate how we can simultaneously infer quantitatively, both the thermodynamic force field acting on the system, as well as the exact rate of entropy production. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, before applying it to the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. Our scheme hence provides a means, potentially exact for a large class of systems, to get a quantitative estimate of the entropy produced in maintaining a non-equilibrium system in a steady state, directly from experimental data.