  Energy exchange processes play a crucial role in the early Universe,
affecting the thermal balance and the dynamical evolution of the primordial
gas. In the present work we focus on the consequences of a non-thermal
distribution of the level populations of H$_2$: first, we determine the
excitation temperatures of vibrational transitions and the non-equilibrium heat
transfer; second, we compare the modifications to chemical reaction rate
coefficients with respect to the values obtained assuming local thermodynamic
equilibrium; third, we compute the spectral distortions to the cosmic
background radiation generated by the formation of H$_2$ in vibrationally
excited levels. We conclude that non-equilibrium processes cannot be ignored in
cosmological simulations of the evolution of baryons, although their
observational signatures remain below current limits of detection. New fits to
the equilibrium and non-equilibrium heat transfer functions are provided.
