# Thermodynamics of quantum systems programmed by classical circuitry

The "thermal operations" (TO) framework developed in past works is used to model the evolution of microscopic quantum systems in contact with thermal baths. Here we extend the TO model to describe hybrid devices consisting of quantum systems controlled by macroscopic or otherwise classical elements external to the system-bath setup. We define the operations of such hybrid devices as conditioned thermal operations (CTO), and their deviation from thermal equilibrium as conditional athermality. We develop the resource theory of conditional athermality, including its characterization, quantification, and manipulation. We find that our formalism unifies those of thermo-majorization (M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2013) and conditional majorization (G. Gour et al., arXiv:1506.07124, 2015). After introducing conditional athermality monotones, we find necessary and sufficient conditions for single-copy resource conversion, as well as the asymptotic rate of many-copy conversion. As an application, we derive the conditions for probabilistic conversion of athermality, and find them to be analogous to results on stochastic entanglement manipulation (D. Jonathan and M. Plenio, Phys. Rev. Lett., 83:1455, 1999; G. Vidal, Phys. Rev. Lett., 83:1046, 1999).

**Comments:**Feedback appreciated! 8 pages main (3 figures) + 6 pages supplement (2 figures)

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