DERIVATION OF THE BOLTZMANN EQUATION AS A TEST OF KINETIC-THEORETICAL SCHEMES

The derivation of the Boltzmann equation from the Liouville equation can be a means of testing the feasibility of a kinetic-theoretical scheme, since the Boltzmann equation is known as empirically plausible. From this viewpoint, one investigates kinetic-theoretical schemes deriving the Boltzmann equation. One may derive the Boltzmann equation consistently by considering the Liouville equation to govern the distribution of a system in the phase space which is not symmetric in the microscopic sense. On the other hand, one cannot derive the equation consistently on the assumption of symmetry of the distribution the Boltzmann collision integral is not compatible with the symmetry assumption.