where Φ Φ i j ( q i , q j ) is the pair potential for interaction between particles, and Φ Φ ext ( q i ) is the external-field potential. By integration over part of the variables, the Liouville equation can be transformed into a chain of equations where the first equation connects the evolution of one-particle probability density function with the two-particle probability density function, second equation connects the two-particle probability density function with the three-particle probability density function, and generally the s -th equation connects the s -particle probability density function