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Several definitions of heat and work exist and they disagree.","posed_since":"","precise":"For $H = H_S(t) + H_B + H_I$ with the norm of $H_I$ comparable to the system energy scale, find definitions of internal energy $U$, work $W$ and heat $Q$ of the system that satisfy the first law, a second law (Clausius inequality or nonnegative entropy production), reduce to weak-coupling results, and are measurable by local operations; or prove that no definition satisfies all of these.","problem_ref":"5d92bcf1e9b03a8e6d4c8385bd6e47e240bb1bebb88df4d5b2a80bb7275c464a","references":"","settled_by":"A theorem identifying the unique definition under stated axioms, or an impossibility proof, checked on an exactly solvable model such as Caldeira-Leggett.","status_note":"2025-2026 papers (e.g. arXiv:2502.19418, arXiv:2605.19941) compare inequivalent definitions; none is accepted as standard.","title":"Defining heat and work for strongly coupled quantum 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