Quantum thermodynamics of overdamped modes in local and spatially dispersive materials

The quantum thermodynamical properties of (quasi-normal) overdamped electromagnetic modes (eddy currents) are investigated in the context of the magnetic Casimir-Polder interaction. The role of the material response in terms of spatially local and nonlocal material models is discussed. In particular, the focus is set on the system's entropy in the limit of low temperatures. In specific circumstances the spatially local (Drude) model reveals an "entropy defect", while spatial dispersion leads to a more regular behavior. We present a detailed description of this phenomenon and of the different mechanisms at work in the system with regard to the eddy modes' properties. Extensively discussing classical and quantum features, we relate our results to the wide range of literature and draw intriguing connections to seemingly distant fields as, e.g., the theory of magnetohydrodynamics and superconductivity.