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The quantum thermodynamical properties of (quasi-normal) overdampedelectromagnetic modes (eddy currents) are investigated in the context of themagnetic Casimir-Polder interaction. The role of the material response in termsof 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. Inspecific circumstances the spatially local (Drude) model reveals an "entropydefect", while spatial dispersion leads to a more regular behavior. We presenta detailed description of this phenomenon and of the different mechanisms atwork in the system with regard to the eddy modes' properties. Extensivelydiscussing classical and quantum features, we relate our results to the widerange of literature and draw intriguing connections to seemingly distant fieldsas, e.g., the theory of magnetohydrodynamics and superconductivity.

Quantum thermodynamics of overdamped modes in local and spatially dispersive materials