The spectrum of massless bosonic and fermionic fluids satisfying the e
quation of state p = (gamma - 1)rho is derived using elementary statis
tical methods. As a limiting case, the Lorentz-invariant spectrum of t
he vacuum (gamma = 0, p = -rho) is deduced. These results are in agree
ment with our earlier derivation for bosons using thermodynamics and s
emiclassical considerations.