Using N-body/hydrodynamic simulations, the influence of non-equipartition processes on the thermal and dynamical properties of cosmological baryonic gas is investigated. We focus on a possible departure from equilibrium between electrons, ions and neutral atoms in low temperature (10⁴-10⁶ K) and weakly ionized regions of the intergalactic medium. The simulations compute the energy exchanges between ions, neutrals and electrons, without assuming thermal equilibrium. They include gravitation, shock heating and cooling processes, and follow self-consistently the chemical evolution of a primordial composition hydrogen-helium plasma without assuming collisional ionization equilibrium. At high redshift, a significant fraction of the intergalactic medium is found to be warmer and weakly ionized in simulations with non-equipartition processes than in simulations in which the cosmological plasma is considered to be in thermodynamic equilibrium. With a semi-analytical study of the out of equilibrium regions we show that, during the formation of cosmic structures, departure from equilibrium in accreted plasma results from the competition between the atomic cooling processes and the elastic processes between heavy particles and electrons. Our numerical results are in agreement with this semi-analytical model. Therefore, since baryonic matter with temperatures around 10⁴ K is a reservoir for galaxy formation, non-equipartition processes are expected to modify the properties of the objects formed.