Article [16] On the irreversible thermodynamic behavior of electron Swarms Abstract: In the framework of the irreversible thermodynamics the problem of elastic collisions of electron swarms with monatomic gases is studied under temperature relaxation in the presence of a uniform external electric field. The correction of the electrons velocity distribution function expressed in terms of Sonin polynomials is inserted into the Boltzmann kinetic equation considering the neutral gas as a heat bath. The Hilbert method is applied in the H-theorem to yield analytical expressions for the transport quantities such as the drift velocity, mobility, the coefficients of thermal diffusion and thermal conductivity. It is verified that the entropy production sign is positive with respect to the controlling parameters namely the temperature ratio and the external electric field.