{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"9018a517d1aa1cef83ad623480042e3b3ba1f4b4ecbfa2d6946620d539156523","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","ae4ecb85ec476ab2c7477e3c8cb53ccc9cdde05656075fc5faeac679dd015d50"],"salt":"6a1ad6c1d938882b52ef10bd694a95120bcbea79fba85e729b8a60b65edcc336","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qi.quantum-thermo.clock-precision-entropy","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"ae4ecb85ec476ab2c7477e3c8cb53ccc9cdde05656075fc5faeac679dd015d50","relation":"special_case"}],"plain":"A clock must waste energy to tick, and classical clocks become steadier only in proportion to the waste. A 2025 theory paper showed quantum clocks can become steadier exponentially faster, so the ultimate limit is open.","posed_since":"2017","precise":"For an autonomous clock driven by thermal baths, let $N = \\mu^2 / \\sigma^2$ be the precision of the waiting time between ticks and $\\Sigma$ the entropy produced per tick ($k_B = 1$); classical Markov clocks obey $N \\le \\Sigma / 2$. Meier et al. (Nature Physics 2025, arXiv:2407.07948) found a coherent many-body clock with $N$ growing exponentially in $\\Sigma$. Determine the optimal $N(\\Sigma, d)$ for clocks of Hilbert-space dimension $d$, and demonstrate $N > \\Sigma / 2$ experimentally.","problem_ref":null,"references":"","settled_by":"A proved upper bound on $N$ matched by a construction, plus an implementation exceeding $N = \\Sigma / 2$.","status_note":"Exponential scaling of $N$ with $\\Sigma$ was shown theoretically (Meier et al., Nature Physics 2025); a September 2026 superconducting experiment reached a current TUR ratio $1.71 \\pm 0.17$ below the classical value 2 (arXiv:2609.37149), but no clock with $N > \\Sigma/2$ has been reported; the optimal scaling is unknown.","title":"Maximal precision of a quantum clock per unit entropy","topic_ref":"742b38754a9f76dd32b7efe7d343f52ad880f5cd0826c1581b9a9198dd522611"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"88f21f85a8e828b5563bc09df37a7b2ab3b835f1b3664f435695e0ee99844a17","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"5a2c927b08fabb8710b8418a9cc84266742c27538703516e017dc0c42412a587","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"t3xSIVUUZOu4TZMFrW7AaHCF-LbroIIvZlGfTJTwL-opQebDV8ijbLIQUr9Yqn7-Qm9OQg5ZuTkvse-tIcVQAQ"},"schema":"pubphys.envelope/1"},"record_hash":"88f21f85a8e828b5563bc09df37a7b2ab3b835f1b3664f435695e0ee99844a17","leaf_index":2044}