bibkey: lostaglio2015coherence authors: Matteo Lostaglio; David Jennings; Terry Rudolph year: 2015 title: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy doi: 10.1038/ncomms7383 url: https://arxiv.org/abs/1405.2188 claim: Thermal operations obey time-translation covariance, and coherent thermodynamic processes require constraints beyond free-energy monotones. strata_touched:

• D5/S3/Quantum/Dynamics/HamiltonianEffectCompletionGenerator license: citation-only triage: anchor

Dynamics and thermal calibration impose different conditions

The arXiv PDF was read at Theorem 1, the surrounding time-asymmetry discussion, and the Methods proof of equation (15). Thermal operations form a strict subset of operations symmetric under the Hamiltonian time translations. The paper also treats classically controlled changes of Hamiltonian in its Methods discussion.

The unified theory uses covariance as an independently stated requirement for a recovery map between different input and output Hamiltonians. For commuting conditional Hamiltonians, the off-diagonal recovery block is restricted to an exact energy-gap eigenspace. The resulting coherence maximum is derived in that restricted recovery class. It is not claimed that covariance and Gibbs calibration together characterize all thermal operations.

In the two-branch Ising example, thermal-only optimization, exact-autonomous optimization and finite-time approximate covariance are three separate tasks. No empirical frequency tolerance is promoted to exact degeneracy, and no work cost follows from the channel calculation alone. The existing Scribe handle provides the commutator-dynamics interface, not a proof of these paper-level optimization claims.