  The Gibbs approach to statistical mechanics is based upon probability distributions, p(X3N, P3N), over the state space, rather than the properties of individual microstates. The Gibbs entropy of the distribution is defined by SG = −k ∫ p(X3N, P3N) ln p(X3N, P3N) dX3NdP3N. If the state space is divided into a number of distinct macrostates, Ri, then the Gibbs entropy of the ith macrostate is