QI In the literature: open

Tight thermodynamic uncertainty relation for quantum machines

In plain words

In small classical machines, making a current steadier always costs extra wasted heat according to a fixed rule. Quantum machines can beat that rule, but by how much is unknown.

Precise statement

For a time-integrated current $J$ in a nonequilibrium steady state with total entropy production $\Sigma$ ($k_B = 1$), classical Markov dynamics obey $\operatorname{Var}(J) / \langle J\rangle^2 \ge 2 / \Sigma$. For quantum steady states (Lindblad dynamics, coherent transport), determine the tightest universal lower bound on $\operatorname{Var}(J) / \langle J\rangle^2$ as a function of $\Sigma$ and of system data such as Hilbert-space dimension $d$ or dynamical activity.

What would settle it

A proved bound together with an explicit model that saturates it.

Status in the literature

Unverified note

Several quantum bounds appeared in 2024-2026 (e.g. arXiv:2505.09973); a September 2026 superconducting thermal machine measured a TUR ratio $\operatorname{Var}(J) \Sigma / \langle J\rangle^2 = 1.71 \pm 0.17$, below the classical value 2 (arXiv:2609.37149); the tight quantum bound is unknown.