Connections between the thermodynamics of classical electrodynamic systemsand quantum mechanical systems for quasielectrostatic operations

The thermodynamic behavior is analyzed of a single classical charged partic le in thermal equilibrium with classical electromagnetic thermal radiation, while electrostatically bound by a fixed charge distribution of opposite s ign. A quasistatic displacement of this system in an applied electrostatic potential is investigated. Treating the system nonrelativistically, the cha nge in internal energy, the work done, and the change in caloric entropy ar e all shown to be expressible in terms of averages involving the distributi on of the position coordinates alone. A convenient representation for the p robability distribution is shown to be the ensemble average of the absolute square value of an expansion over the eigenstates of a Schrodinger-like eq uation, since the heat flow is shown to vanish for each hypothetical "state ". Subject to key assumptions highlighted here, the demand that the entropy be a function of state results in statistical averages in agreement with t he form in quantum statistical mechanics. Examining the very low and very h igh temperature situations yields Planck's and Boltzmann's constants. The b lackbody radiation spectrum is then deduced. From the viewpoint of the theo ry explored here, the method in quantum statistical mechanics of statistica lly counting the "states" at thermal equilibrium by using the energy eigenv alue structure, is simply a convenient counting scheme, rather than actuall y representing averages involving physically discrete energy states.