We now introduce Boltzmann’s famous formula (up to an additive constant) for what we might call the “Boltzmann entropy” \(S_B\): \[ S_B (M(X)) = k \log \lvert\Gamma_M\rvert \] where \(\lvert\Gamma_M\rvert\) is the volume in \(\Gamma\) associated with the macrostate \(M\), \(X\) is the microstate of the system, and \(k\) is Boltzmann’s constant. \(S_B\) provides a relative measure of the amount of \(\Gamma\) corresponding to each \(M\).