Introduction Differential expression of the first principle of thermodynamics: d E = T d S − p d V {\displaystyle dE=TdS-pdV} Boltzmann relation between entropy S {\displaystyle S} and number of microstates at a given energy g ( E ) {\displaystyle g(E)} : S = k log ( g ( E ) ) {\displaystyle S=k\log(g(E))} The above defines an extensive property of the system, i.e. if we have two subsystems at S 1 , S 2 {\displaystyle S_{1},S_{2}} then S = S 1 + S 2 = k log ( g 1 g 2 ) = k log ( g ) {\displaystyle S=S_{1}+S_{2}=k\log(g_{1}g_{2})=k\log(g)} .