Kinetic-Energy Corrections to Klein's Theorem for the Thermodynamic Functions of a Plasma

It is shown that the average thermal energy of a system of N free electrons and N free protons with density n=N/V and temperature T has the form E=2N[3/2kT+Tf(η)+f₁(n, T)+f₂^'(n, T)], where f, the leading term in the electrostatic energy, is an arbitrary function of η=Tn^-1/3 in agreement with the original Klein theorem. f₁ is a kinetic-energy correction which is related to the electrostatic energy f₂^' by the differential equation ${-}n/T{{∂}}{{∂}n}{({f}₁+{{f}₂}^{{'}})}T=T/3{{∂}}{{∂}T}{({2{f}₁+{{f}₂}^{{'}}}{T})}ₙ.$ Some consequences of this result are discussed.