I am reading Planck's work on black-body radiation. In the paper on the page 19 it is said that the expression
$$R_\nu=\frac{\nu^2}{c^2}U\tag1$$
where $R_\nu$ is the intensity of a linearly polarised light, is an expression of (electromagnetic) entropy maximum. In other words, it is a stationary state, i.e.
$$dS = 0, \qquad \frac{d^2S}{dU^2} < 0 \,.$$
I don't understand why $(1)$ would be a statement of entropy maximum. He defines the energy of an oscillator with frequency $\nu$ as
$$U=b\space\nu\space \exp\left(\frac{-a\space\nu}{T}\right)\tag2$$
and the entropy as
$$S=-\frac{U}{a\nu}log\frac{U}{eb \nu};\quad e= 2.71828...\tag3$$
I don't know how prove that $(1)$ $\implies$ $dS=0$.
Also, the entropy function $(3)$ is decreasing as $U$ is increasing; Does that make sense?
I tried differentiating Equation $(3)$ with respect to $U$ twice and got
$$\frac{\partial^2 S}{\partial U^2}= -\frac{1}{a\nu U}$$
but I don't know hot to connect it with $(1)$ and obtain $R_\nu$.
