Localizing entropy production along non-equilibrium trajectories

An important open problem in nonequilibrium thermodynamics is the quantification and spatiotemporal localisation of entropy production in complex processes from experimental data. Here we address this issue through a data-driven approach that combines the recently developed short-time thermodynamic uncertainty relation based inference scheme with machine learning techniques. Our approach leverages the flexible function representation provided by deep neural networks to achieve accurate reconstruction of high-dimensional, potentially time-dependent dissipative force fields as well as the localization of fluctuating entropy production in both space and time along nonequilibrium trajectories. We demonstrate the versatility of the framework through applications to diverse systems of fundamental interest and experimental significance, where it successfully addresses distinct challenges in localising entropy production.