{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"2827e8a68469984ec78e1e65c676ea9ce9e7b17c14465ae8240d2617f946a554","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ae2befcb4a507454e4d4474d5a6c55319686658703d28100f379c1a156e7b3d4","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qi.quantum-thermo.quantum-tur","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"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.","posed_since":"","precise":"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.","problem_ref":null,"references":"","settled_by":"A proved bound together with an explicit model that saturates it.","status_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.","title":"Tight thermodynamic uncertainty relation for quantum 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