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In classical thermodynamics, the velocity distribution function of particles is always Maxwell distributionfor any density. This is due to the fact that the dependences on the pulses and coordinates in theexpression for the total energy are separated. Integration over coordinates leads to the appearance of aconfiguration integral, and the remaining part is divided into the product of Maxwell distributionfunctions. In the case of formation of bound states (molecules) in an atomic gas, the full phase space ofthe relative motion of two particles is divided into two parts. The first corresponds to negative energies ofrelative motion (molecular component), and the second to positive (free atoms). The velocity distributionfunction remains Maxwellian, if we ignore the fact of separation of the phase space. It can be assumedthat for free atoms the velocity (kinetic energies) distribution may be different from Maxwell. Forplasmas, 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 isestimated.

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