  Generalized empirical currents represent a vast class of thermodynamic
observables of mesoscopic systems. Their fluctuations satisfy the thermodynamic
uncertainty relations (TURs), as they can be bounded by the average entropy
production. Here, we derive a general closed expression for the hyperaccurate
current in discrete-state Markovian systems, i.e., the one with the least
fluctuations, for both discrete- and continuous-time evolution. We show that
its associated hyperaccurate bound is generally much tighter than the one given
by the TURs, and might be crucial to providing a reliable estimation of the
average entropy production. We also show that one-loop systems (rings) exhibit
a hyperaccurate current only for finite times, highlighting the importance of
short-time observations. Additionally, we derive two novel bounds for the
efficiency of work-to-work converters, solely as a function of either the input
or the output power. Finally, our theoretical results are employed to analyze a
6-state model network for kinesin, and a chemical system in a thermal gradient
exhibiting a dissipation-driven selection of states.
