The conditions for statistical equilibrium between atoms, electrons and radiation

Abstract

The principle of the reversibility of atomic processes was introduced by Klein and Rosseland for the case of non-radiative encounters between atoms and free electrons. These authors pointed out that it is necessary for thermodynamic equilibrium in an enclosure in which the transference of atoms to higher stationary states takes place by collisions with free electrons without the emission or absorption of radiation, that the reverse process by which an atom falls from a higher to a lower stationary state, the whole of the surplus energy being spent in increasing the kinetic energy of a colliding electron, must occur to just a sufficient extent to balance the first process. It cannot, however, be proved from thermodynamic considerations alone that every process that occurs in an assembly in statistical equilibrium is exactly balanced by the reverse process taking place with the same frequency, since, as has been shown by Fowler, there may be cycles of inseparable processes, each of which does not balance individually, although the whole cycle forms a “unit mechanism” which balances by itself in any assembly in statistical equilibrium. It seems plausible, however, to suppose that all atomic processes are reversible, or, more exactly, that if after any encounter all the velocities are reversed, then the whole process would just repeat itself backwards, the systems finally leaving the scene of action being the same as the original systems in the first process and having the reverse velocities. With this assumption, to which there are no known exceptions, each kind of encounter must be just as likely to occur as its converse in which every velocity has changed sign, the whole process taking place backwards, since there is now perfect symmetry between past and future time. This converse is not the same as the reverse process referred to above, in which the velocities before and after the encounter are the same as the velocities after and before the original encounter respectively. What have been called the converse and reverse encounters are, however, related in such a way that one can be obtained from the other by successive reflections in three mutually perpendicular mirrors at rest relative to the assembly as a whole, and so their frequencies of occurrence must be equal, since the assembly is everywhere isotropic. This proves that every kind of encounter occurs with the same frequency as the reverse encounter, the two together leaving unaltered both the numbers of the various kinds of systems, and also their distributions in velocity or momentum. This condition is sufficient for statistical equilibrium, and on the above-made assumption of the reversibility of the encounters, it is necessary.