Energy of a plasma in the classical limit

When lambda(T) << d(T), where lambda(T) is the de Broglie wavelength and d( T) is the distance of closest approach of thermal electrons, a classical an alysis of the energy of a plasma can be made. In all the classical analysis made until now, it was assumed that the frequency of the fluctuations w << T, (k(B) = h overbar = 1). Using the fluctuation-dissipation theorem, we e valuate the energy of a plasma, allowing the frequency of the fluctuations to be arbitrary. We find that the energy density is appreciably larger than previously thought for many interesting plasmas, such as the plasma of the Universe before the recombination era.