Spectrum of $\gamma$-Fluids: A Statistical Derivation

The spectrum of massless bosonic and fermionic fluids satisfying the equation of state $p=(\gamma -1)\rho$ is derived using elementary statistical methods. As a limiting case, the Lorentz invariant spectrum of the vacuum ($\gamma=0, p=-\rho$) is deduced. These results are in agreement with our earlier derivation for bosons using thermodynamics and semiclassical considerations.