Temperature transform of the Boltzmann equation

The authors define an integral transform of the energy distribution function for an isotropic and homogeneous diluted gas. It may be interpreted as a linear combination of equilibrium states with variable temperatures. They show that the temporal evolution features of the distribution function are determined by the singularities of this temperature transform. They compare the relaxation to the equilibrium process for Maxwell and very hard-particle interaction models, finding many basic discrepancies. Finally, the authors formulate an alternative approach, which is given by an N-pole approximation with a clear physical meaning