What is Boltzmann entropy?

The statistical entropy of a macrostate is

The logarithm makes entropy additive where multiplicities multiply: for independent systems $\Omega = \Omega_1\Omega_2$ and $S = S_1 + S_2$; Boltzmann’s constant calibrates the count to the kelvin-and-joule units thermodynamics had already chosen. This $S$, we will verify, is the entropy of the Year 1 volume’s second law — now with a microscopic meaning: entropy measures, in logarithmic currency, how many ways the macrostate can be realised.