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Coupling a system to two different baths can lead to novel phenomena escapingthe constraints of thermal equilibrium. In quantum materials inside opticalcavities, this feature can be exploited as electrons and cavity-photons areeasily pulled away from their mutual equilibrium, even in the steady state.This offers new routes for a non-invasive control of material properties andfunctionalities. We show how the absence of thermal equilibrium betweenelectrons and photons leads to qualitative modifications of the material'sproperties, as the standard Sommerfeld expansion for observables near the Fermisurface is modified by a leading-order correction linearly proportional to thetemperature difference. This modification arises from the breaking of asymmetry underlying the thermal description and thus can't be predicted withinthe latter.

Non-thermal electron-photon steady-states in open cavity-quantum-materials