Multidimensional entropic bound: Estimator of entropy production for Langevin dynamics with an arbitrary time-dependent protocol

Entropy production (EP) is a key quantity in thermodynamics, and yet measuring EP has remained challenging task. Here we introduce an estimator, called multidimensional entropic bound (MEB), utilizing ensemble of trajectories. The MEB can accurately estimate the overdamped Langevin systems with arbitrary time-dependent protocol. Moreover, it provides unified platform to underdamped under certain conditions. In addition, computationally efficient because optimization unnecessary. We apply our developed estimator three physical driven by protocols pertaining experiments using optical tweezers: A dragged Brownian particle, pulling process harmonic chain, unfolding RNA hairpin. Numerical simulations confirm validity efficiency method.