{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"23215729b9c5515083df2b2727b38dd9e9138aaa278d193589b9ce5048aef96c","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"c45affa16e189a7e67c7e53efee290fa86d5aa36a9c51823735c8d2c1fec76a9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qi.quantum-thermo.battery-charging-advantage","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"A quantum battery is a set of N small quantum cells that store energy; charging them together with collective interactions may be faster than charging each cell separately. How that speed-up can grow with N under realistic, few-body interactions is disputed.","posed_since":"","precise":"For $N$ identical cells with $H_{0}=\\sum_i h_i$, a charging Hamiltonian $V(t)$ that is a sum of at most $k$-body terms of bounded norm, and charging power $P=(E(\\tau)-E(0))/\\tau$, define the advantage $\\Gamma=P_{\\mathrm{collective}}/P_{\\mathrm{parallel}}$. Gyhm, Safranek and Rosa (PRL 2022) proved that $\\Gamma$ cannot grow extensively in $N$ without global operations; determine the maximal scaling of $\\Gamma$ with N and k under stated constraints (bounded energy per cell, bounded interaction strength, geometric locality), and whether any physical constraint set allows $\\Gamma$ to grow with $N$ at fixed $k$.","problem_ref":null,"references":"","settled_by":"A proved upper bound on $\\Gamma(N, k)$ under stated constraints, matched by an explicit charging protocol.","status_note":"A Physical Review Letters article titled 'Super-extensive charging power in the absence of global operations' appeared in September 2026 (doi:10.1103/vjft-c6fp); its assumptions and their relation to the 2022 bound were not checked here.","title":"Is super-extensive charging power possible with few-body 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