Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser

TL;DR

This paper investigates how quantum coherence in a three-level maser can violate the traditional thermodynamic uncertainty relation, revealing quantum advantages and complex fluctuation behaviors beyond classical limits.

Contribution

It analytically demonstrates TUR violations in a quantum heat engine due to coherence effects, surpassing classical bounds and extending the understanding of quantum thermodynamics.

Findings

Quantum coherence can suppress fluctuations, indicating a quantum advantage.

TUR violations occur beyond steady-state coherence, involving non-steady-state effects.

The system often operates near the conventional TUR limit, with violations being relatively common.

Abstract

Nanoscale heat engines are subject to large fluctuations which affect their precision. The Thermodynamic Uncertainty Relation (TUR) provides a trade-off between output power, fluctuations and entropic cost. This trade-off may be overcome by systems exhibiting quantum coherence. This letter provides a study of the TUR in a prototypical quantum heat engine, the Scovil & Schulz-DuBois maser. Comparison with a classical reference system allows us to determine the effect of quantum coherence on the performance of the heat engine. We identify analytically regions where coherence suppresses fluctuations, implying a quantum advantage, as well as regions where fluctuations are enhanced by coherence. This quantum effect cannot be anticipated from the off-diagonal elements of the density matrix. Because the fluctuations are not encoded in the steady state alone, TUR violations are a consequence of coherence that goes beyond steady-state coherence. While the system violates the conventional TUR, it adheres a recent formulation of a quantum TUR. We further show that parameters where the engine operates close to the conventional limit are prevalent and TUR violations in the quantum model not uncommon.