Quantum Coherence as a Thermodynamic Resource Beyond the Classical Uncertainty Bound

Abstract

The precision of nonequilibrium thermodynamic systems is fundamentally limited, yet how quantum coherence shapes these limits remains largely unexplored. A general theoretical framework is introduced that explicitly links quantum coherence to thermodynamic uncertainty relations. By defining a coherence-sensitive measure, it is shown that quantum effects can relax the classical trade-off between the entropy production and the current fluctuations, enabling the precision beyond classical bounds. Application to a three-level quantum maser illustrates the framework in a concrete setting. These results establish quantum coherence as a genuine thermodynamic resource and provide a unified perspective connecting classical and quantum approaches to nonequilibrium thermodynamics.

Figures (1)

• Figure 1: (a) Schematic diagram of the quantum Scovil--Schulz-DuBois (SSDB) three-level maser. The thermodynamic uncertainty relation (TUR) $D\sigma/J^{2}$ (dash-dotted red line) for the quantum SSDB three-level maser, the TUR $\mathcal{Q}^{\text{cl }}$ (solid black line) of the classical reference system, the coherence bound $2\left(1+\psi\right)^{2}$ (short-dashed blue line), and the quantum TUR bound $\mathcal{\mathrm{\Xi}\mathrm{=\frac{\sigma}{\Upsilon+\Psi}}}$ (dashed green line) are plotted as functions of (a) the detuning $\Delta$ with $n_{c}=0.027,$ and (c) the bath population $n_{c}$ with $\Delta=0$. (d) The scatter plots of $2\left(1+\psi\right)^{2}$(red circles), $\mathcal{Q}^{\text{cl }}$(blue triangles), and $\mathrm{\Xi}$ (green cubes) against $D\sigma/J^{2}$, where $\Delta$ is randomly chosen from -1.5 to 1.5, $\Omega$ is randomly chosen from 0.01 to 0.8, and $n_{c}=0.027$. The remaining parameters are fixed at $\gamma_{c}=2,\gamma_{h}=0.1$, $\Omega=0.15$, and $n_{h}=5$.