Hyperaccurate thermoelectric currents

Thermodynamic currents, such as energy, heat, and entropy production, can fluctuate significantly at the nanoscale. However, some fluctuate less than others. Hyperaccurate currents are defined as those which fluctuate the least, in the sense that they maximize the signal-to-noise ratio (precision). In this Letter we analytically determine what are the hyperaccurate currents in quantum thermoelectrics, modeled by coherent transport in the Landauer-B\"uttiker formalism. Our results yield a tight and general bound on precision, which replace the classical thermodynamic uncertainty relations, that can be violated in quantum thermoelectrics. They also allow us to address the question of how close to hyperaccurate is a given current. We illustrate our findings for smooth boxcar functions, and for a double quantum dot operating as a thermal machine. In the latter, we use our results to establish the parameter ranges for which the output power of an autonomous engine can become hyperaccurate arbitrarily far from equilibrium.