Assuming that the entropy (S) and the statistical number (Omega) of a physical system are related through

Question:

Assuming that the entropy $S$ and the statistical number $\Omega$ of a physical system are related through an arbitrary functional form

\[
S=f(\Omega),
\]

show that the additive character of $S$ and the multiplicative character of $\Omega$ necessarily require that the function $f(\Omega)$ be of the form (1.2.6).

Fantastic news! We've Found the answer you've been seeking!