
\sect{Entropy, additivity}

%Baruch's  A01

Assume that the entropy S and the number of states in
phase space ${\Omega}$ of a physical system are related through an
arbitrary function, ${S=f\left(\Omega \right)}$. Show that the
additive character of ${S}$ and the multiplicative character of
${\Omega}$ \emph{necessarily} require that ${f\left(\Omega \right
) \sim \ln \Omega}$. 

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