Defining heat and work for strongly coupled quantum systems
In plain words
When a small quantum system interacts strongly with its surroundings, the energy stored in the interaction cannot be cleanly assigned to either side. Several definitions of heat and work exist and they disagree.
Precise statement
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.
What would settle it
A theorem identifying the unique definition under stated axioms, or an impossibility proof, checked on an exactly solvable model such as Caldeira-Leggett.
Status in the literature
Unverified note
2025-2026 papers (e.g. arXiv:2502.19418, arXiv:2605.19941) compare inequivalent definitions; none is accepted as standard.