  Cosmic very small dust grains (VSGs) contain 100 to 10,000 atoms, making it a
mesoscopic system with specific thermal and optical characteristics due to the
finite number of atoms within each grain. This paper focuses on graphite VSGs
which contain free electrons. The energy level statistics devised by Kubo
(1962, J.Phys.Soc.Jpn., 17, 975-986) were used for the first time to understand
the thermal properties of free electrons in graphite VSGs. We showed that the
shape irregularity of the grains allows graphite VSGs to absorb or emit photons
at sub-millimeter wavelengths or longer; otherwise, the frequency is limited to
above a few THz. Additionally, we considered the decrease in Debye temperature
due to the surface effect. VSGs have an extremely small volume, resulting in
limited thermal energy storage, especially at low temperatures. Since a VSG is
able to emit a photon with energy smaller than its internal energy, this
determines the maximum frequency of the emitted photon. We developed a
Monte-Carlo simulation code to track the thermal history of a dust grain,
considering the stochastic heating from the absorption of ambient photons and
radiative cooling. This approach was applied to the interstellar environment to
compute the spectral energy distributions from the interstellar graphite dust
grains. The results showed that graphite VSGs emit not only the mid-infrared
excess emission, but also a surplus emission from sub-millimeter to millimeter
wavelengths.
