  Entropy production (EP) is a key quantity in thermodynamics, and yet
measuring EP has remained a challenging task. Here we introduce an EP
estimator, called multidimensional entropic bound (MEB), utilizing an ensemble
of trajectories without knowing the details of a given system. MEB is a unified
method in the sense that it is applicable to both overdamped and underdamped
Langevin dynamics, irrespective of the time dependence of the driving protocol.
In addition, MEB is computationally efficient because optimization is
unnecessary. We apply our developed estimator to three physical systems driven
by time-dependent protocols pertaining to experiments using optical tweezers: a
dragged Brownian particle, a pulling process of a harmonic chain, and an
unfolding process of an RNA hairpin. Numerical simulations confirm the validity
and efficiency of our method.
