The power-spectrum tensor in steady-state systems and its role in quantum friction

We derive and classify properties of the power-spectrum tensor for systems in general steady-states, including stationary states not necessarily corresponding to equilibrium configurations. We establish a rigorous connection between the power-spectrum tensor and other quantities that characterize these systems, providing a systematic comparison with their equilibrium counterparts. As a physical application, we investigate the problem of quantum friction, describing the contactless quantum-electrodynamic drag acting on a particle moving in close proximity to material bodies at zero temperature. Specifically, we demonstrate how including additional information about the system's physical properties facilitates the derivation of more precise constraints on the power spectrum and its functional dependencies.