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We investigate the relaxation of internal temperature and the concept of volume viscosity in nonequilibrium gas models derived from the kinetic theory. We first investigate a nonequilibrium gas model with two temperatures-translational and internal-where the volume viscosity is absent. We establish that, in a relaxation regime, the temperature difference becomes proportional to the divergence of the velocity fields and define a nonequilibrium, multitemperature, volume viscosity coefficient. We next analyze the convergence of the two temperature model towards the one temperature model when the relaxation is fast. We then investigate a nonequilibrium two temperature gas model with a fast and a slow internal energy mode. We establish that, in a relaxation regime, there are four contributions to the volume viscosity, namely the fast internal mode volume viscosity, the slow internal mode volume viscosity, the relaxation pressure and the perturbed source term. In the thermodynamic equilibrium limit, the sum of these four terms converges toward the one-temperature two-mode volume viscosity. We finally perform Monte Carlo simulations of spontaneous fluctuations near thermodynamic equilibrium. The numerical results obtained from the Boltzmann equation are compared to the predictions of the one and two temperature fluid models and the agreement between theory and calculations is complete.

State-to-state approaches are used to shed light on (a) thermodynamic and transport properties of LTE plasmas, (b) atomic and molecular plasmas for aerospace applications and (c) RF sustained parallel plate reactors. The efforts made by the group of Bari in the kinetics and dynamics of electrons and molecular species are discussed from the point of view of either the master equation approach or the molecular dynamics of elementary processes. Recent experimental results are finally rationalized with a state-to-state kinetics based on the coupling of vibrational kinetics with the Boltzmann equation for the electron energy distribution function.