  Systems coupled to multiple thermodynamic reservoirs can exhibit
nonequilibrium dynamics, breaking detailed balance to generate currents. To
power these currents, the entropy of the reservoirs increases. The rate of
entropy production, or dissipation, is a measure of the statistical
irreversibility of the nonequilibrium process. By measuring this
irreversibility in several biological systems, recent experiments have detected
that particular systems are not in equilibrium. Here we discuss three
strategies to replace binary classification (equilibrium versus nonequilibrium)
with a quantification of the entropy production rate. To illustrate, we
generate time-series data for the evolution of an analytically tractable
bead-spring model. Probability currents can be inferred and utilized to
indirectly quantify the entropy production rate, but this approach requires
prohibitive amounts of data in high-dimensional systems. This curse of
dimensionality can be partially mitigated by using the thermodynamic
uncertainty relation to bound the entropy production rate using statistical
fluctuations in the probability currents.
