  The quantum oscillator thermodynamic actions are the conjugate intensive
parameters for the frequency in any frequency changing process. These
oscillator actions fulfill simple Riccati equations. Interesting Darboux
transformations of the fundamental Planck and pure vacuum actions are discussed
here in some detail. It is shown that the one-parameter
"Darboux-Transformed-Thermodynamics" refers to superpositions of boson and
fermion excitations of positive and negative absolute temperature,
respectively. A Darboux generalization of the fluctuation-dissipation theorem
is also briefly sketched
