Probability distribution for a lattice gas model

The behavior of the probability distribution for a lattice gas obtained in a preciding paper is analyzed in the so-called thermodynamic limit. Two situations, corresponding to cases in which the ratio between the subvolume under consideration and the total volume remains finite or tends to zero, are discussed. The latter case allows us to write the probability distribution in terms of the intensive parameters. The numerical analysis of the probability distribution in this case and the implication of the results in order to explain the features of a liquid-vapor phase transition are reported.