Thermal Purcell effect and cavity-induced renormalization of dissipations

In recent years there has been great interest towards optical cavities as a tool to manipulate the properties and phases of embedded quantum materials. Due to the Purcell effect, a cavity changes the photon phase space and thus the rate of electromagnetic transitions within the material, modifying the exchange rate of heat radiation with the photon environment. Here, I derive a simple expression for the radiative heat power absorbed by the material, investigate how it changes in the presence of a cavity and show that it is enhanced dramatically for appropriate cavity geometries. I compare this effect with typical energy dissipation processes, provide a criterion to establish its impact on the temperature of a material coupled to the cavity and apply it to 1T-TaS$_2$.