Absence and recovery of cost-precision tradeoff relations in quantum transport

TL;DR

This paper investigates how quantum transport systems can violate or restore thermodynamic uncertainty relations depending on transmission engineering, revealing conditions under which cost-precision tradeoffs are absent or reemerge.

Contribution

It demonstrates that engineered transmission functions can eliminate cost-precision tradeoffs in quantum nanojunctions, and shows how realistic models restore these tradeoffs away from ideal conditions.

Findings

Perfect transmission with hard energy cutoffs can violate TUR.

Soft cutoffs or imperfect transmission restore TUR.

Violation of TUR is exponentially suppressed with increased voltage.

Abstract

The operation of many classical and quantum systems in nonequilibrium steady state is constrained by cost-precision (dissipation-fluctuation) tradeoff relations, delineated by the thermodynamic uncertainty relation (TUR). However, coherent quantum electronic nanojunctions can escape such a constraint, showing finite charge current and nonzero entropic cost with vanishing current fluctuations. Here, we analyze the absence, and restoration, of cost-precision tradeoff relations in fermionic nanojunctions under different affinities: voltage and temperature biases. With analytic work and simulations, we show that both charge and energy currents can display the absence of cost-precision tradeoff if we engineer the transmission probability as a boxcar function -- with a perfect transmission and hard energy cutoffs. Specifically for charge current under voltage bias, the standard TUR may be immediately violated as we depart from equilibrium, and it is exponentially suppressed with increased voltage. However, beyond idealized, hard-cutoff energy-filtered transmission functions, we show that realistic models with soft cutoffs or imperfect transmission functions follow cost-precision tradeoffs, and eventually recover the standard TUR sufficiently far from equilibrium. The existence of cost-precision tradeoff relations is thus suggested as a generic feature of realistic nonequilibrium quantum transport junctions.