where is the Liouville operator. It was shown by Kirkwood  that this equation could be converted into the Boltzmann equation for species :
where is a very complex term that contains information regarding the dynamics of a binary encounter between two monatomic molecules, and is the force per unit mass acting on a molecules of species .
1b. The general equation of change
Equation 1.3 may be multiplied by a property B and integrated over all momenta to get the general equation of change forB:
It can be shown that if B is conserved in a collision, then the last term on the right side vanishes.
1c. Special equations of change
We may now write down the equations of change by setting B successively equal to mass , momentum , and energy (keeping in mind that the only energy for monatomic molecules is the kinetic energy—for diatomic molecules, see BSL-2e,