Quantum Coherence as a Thermodynamic Resource Beyond the Classical Uncertainty Bound

Abstract

Thermodynamic uncertainty relations (TURs) establish a fundamental trade-off between current precision and entropy production in nonequilibrium systems, yet the role of genuine quantum coherence in these bounds remains unresolved. Here we develop a general framework that explicitly incorporates quantum coherence into TURs for Markovian open quantum systems. By combining the quantum Cramér-Rao inequality with a Dyson series expansion of the parametrically deformed Lindblad dynamics, we derive a generalized TUR containing a coherence-sensitive correction that naturally separates classical and quantum contributions. The coherent term originates from the off-diagonal components of the nonequilibrium steady-state density matrix and systematically relaxes the classical precision-dissipation bound, allowing enhanced current precision without additional entropy production. Applying our theory to a three-level quantum maser, we demonstrate that steady-state coherence enables precision beyond the classical limit over a broad parameter regime while remaining consistent with the generalized bound. Our results identify quantum coherence as a genuine thermodynamic resource and provide a unified framework bridging classical and quantum uncertainty relations.