Suppose you had an object with such a cloak of invisibility. It must bend light from all directions around itself, creating a shell of light around itself with greater photon density. Place this object in some hot gas giving off blackbody radiation. The light in a shell around the object will be concentrated to a greater intensity than the light in the gas. This can be used to heat an object to a higher temperature than the gas, and a heat engine can be run between that object and a radiator in the gas. This violates the laws of thermodynamics.
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