Finite-size radiation correction due to Casimir effect in black-body cavities

Determine the radiation correction to the black-body internal energy arising from assimilating zero-point energy to the Casimir effect when finite-size effects, cavity geometry, and material properties of the cavity are taken into account; specifically, establish how this correction depends on cavity dimensions and composition beyond the idealized cases and quantify its impact on the Stefan–Boltzmann law predictions.

Background

The paper reviews historical and theoretical developments of black-body internal energy, from Boltzmann’s thermodynamic framework and Planck’s quantum quantization to later treatments incorporating zero-point energy. Including zero-point energy leads to a vacuum catastrophe unless a compensating physical effect is considered.

The Reggiani–Alfinito model (2018) assimilates the zero-point contribution to the Casimir effect, yielding an adjusted internal energy that introduces a radiation correction associated with finite-size effects. The authors emphasize that this correction depends on the cavity’s geometry and material, but its detailed characterization remains incomplete and requires further study.