Hyperaccurate bounds in discrete-state Markovian systems

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