Specific heat in nanostructures by quantum mechanics

Specific heat is thought to be an intensive thermophysical property of a material independent of the dimensions of the body. Today, specific heat at the nanoscale is assumed the same as that of macroscopic bodies. In effect, the classical equipartition theorem of statistical mechanics is assumed at the nanoscale allowing atoms to have heat capacity at all thermal wavelengths. Therefore, classical physics allows submicron wavelengths that can “fit inside” nanostructures to conserve electromagnetic (EM) energy by an increase in temperature. Quantum mechanics (QM) also allows the atom to have heat capacity at submicron wavelength, but only at high temperature. At ambient temperature, the high frequency modes at submicron wavelengths are therefore “frozen out” leaving nanostructures without the heat capacity to increase in temperature to conserve absorbed EM energy. By QM, specific heat vanishes at the nanoscale. Conservation may only proceed by the quantum electrodynamics (QED) induced creation of photons within the nanostructure at a frequency equal to its fundamental EM resonance. Subsequently, QED radiation leaks to the surroundings. Specific heat at the nanoscale is therefore not an intensive property of a material, but rather an extensive property depending on the body dimensions.