We also can see in Figure -bottom that the extended-to-continuous approximations ( ) In the Boltzmann formulation, it is usual to assume that 2 N , yielding ( ) l B T in Eq. . Although this approximation is fully justified for large systems, it has a major conceptual implication: it shifts the system from a Boltzmann to a Gibbs volume description, as made evident by Eqs. ( ) and ( ), where we can see that ( ) ( ) ls BG TT = . Several authors, starting from the Boltzmann formulation, already apply the large N approximation at the level of the number of microstates, Eq. ( ). Because this approximation reduces Eq. ( ) to Eq. ( ), they inadvertently work in the Gibbs volume formulation. ,