Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces.

Abstract

A new fundamental thermodynamic property has been proved for classical electromagnetic zero-point radiation. Aside from a proportionality constant, classical electromagnetic zero-point radiation is shown here to possess the unique spectrum that is suitable for establishing a thermal equilibrium state with a set of fluctuating classical electric dipole harmonic oscillators at the temperature of absolute zero. As a consequence of this analysis, one can see that according to the fundamental thermodynamic definition of absolute zero temperature, the following traditional view in thermodynamics is an unnecessary thermodynamic restriction: namely, that all fluctuating motion and radiation must vanish at T=0 for classical physical systems. Indeed, as shown here, this restriction can violate the third law of thermodynamics if the spectrum reduces to zero by being proportional to T. The analysis in this article involves the calculation of (1) the change in internal energy, (2) the work done, and (3) the heat radiated for a quasistatic displacement of electric dipole nonrelativistic harmonic oscillators immersed in random classical electromagnetic radiation. The calculations include full nonperturbative evaluations of retarded van der Waals thermodynamic functions.