Interpreted in this way, Boltzmann's formula is the most basic formula for the thermodynamic entropy. Boltzmann's paradigm was an ideal gas of N identical particles, of which N i are in the i -th microscopic condition (range) of position and momentum. For this case, the probability of each microstate of the system is equal, so it was equivalent for Boltzmann to calculate the number of microstates associated with a macrostate. W was historically misinterpreted as literally meaning the number of microstates, and that is what it usually means today. W can be counted using the formula for permutations