  A new thermodynamic analysis is presented for the intimate connections
between blackbody radiation and zero-point radiation within classical physics.
First, using the thermodynamic behavior of an oscillator under an adiabatic
change of frequency, we show that the thermodynamic functions can all be
derived from a single function of w/T, analogous to Wien's displacement
theorem. The high- and low-frequency limits allow asymptotic energy forms
involving T alone or w alone, corresponding to energy equipartition and
zero-point energy. It is then suggested that the actual thermodynamic behavior
for a harmonic oscillator is given by the function satisfying the Wien
displacement result which provides the smoothest possible interpolation between
scale-decoupled energy equipartition at low frequency and scale-invariant
zero-point energy at high frequency. This leads to the Planck spectrum. Second,
we turn to radiation in a box with conducting walls and a conducting partition
so that the discrete normal mode structure of the box becomes important. The
contrasting Casimir energies are explored for the Rayleigh-Jeans and zero-point
spectra. The Rayleigh-Jeans spectrum involves no change of energy with
partition position, and the zero-point spectrum involves no change of entropy.
It is suggested that the Planck spectrum with zero-point radiation satisfies a
natural minimum principle which corresponds to greatest independence of the
system energy from the position of the partition for a fixed temperature.
Numerical calculation is used for confirmation. Third, we review the previous
derivations of the Planck radiation spectrum in classical physics, all of which
involve zero-point radiation.
