Casimir Entropy at Low Temperature: What the Third Law Requires of the Vacuum Between Plates

The entropy carried by the electromagnetic vacuum between two plates is a small quantity with a sharp obligation: the third law of thermodynamics requires it to vanish as the temperature falls to zero. This paper evaluates a stated low-temperature model in which the entropy per unit area falls as the square of the temperature, reaching 2.267e-14 joules per kelvin per square metre at room temperature, and it notes the temperature, about 26.0 kelvin, at which the thermal photon scale kT equals the surviving vacuum scale of 2.240 milli-electronvolts. Treatments of the plates that include dissipation in a particular way are known to leave a residual entropy at zero temperature, in tension with the third law; the paper sizes that tension by comparing the residual with the model's values at millikelvin temperatures. The exercise is a computation from stated models, not a measurement, and its conclusion is that thermodynamics disciplines vacuum models at exactly the low energies where gravitational accounting also becomes delicate.