On distribution function of free and bound electrons in equilibrium Coulomb system

In classical thermodynamics, the velocity distribution function of particles is always Maxwell distribution for any density. This is due to the fact that the dependences on the pulses and coordinates in the expression for the total energy are separated. Integration over coordinates leads to the appearance of a configuration integral, and the remaining part is divided into the product of Maxwell distribution functions. In the case of formation of bound states (molecules) in an atomic gas, the full phase space of the relative motion of two particles is divided into two parts. The first corresponds to negative energies of relative motion (molecular component), and the second to positive (free atoms). The velocity distribution function remains Maxwellian, if we ignore the fact of separation of the phase space. It can be assumed that for free atoms the velocity (kinetic energies) distribution may be different from Maxwell. For plasmas, the assumption of the non-Maxwellian velocity distribution function of free electrons was made. The influence of the non-Maxwell electron distribution function on the recombination coefficient is estimated.