Publication 1640

One of the primary problems in statistical mechanics is to find in a system of a large number of freely interacting elements (particles) the distribution of the available energy over all elements which will be observed in most of the cases when the number of elements N1 are counted which possess energies that fall within an “energy-bracket” Ei ± ½δ of width δE; (i = 1, 2, 3, …). In a conservative system in which the number of elements, N, and the available energy, E, are given and remain unchanged, the most probable distribution is, of course, Boltzmann’s distribution function which maximizes the entropy of the system and has the form of a decaying exponential Ni = No exp(-Ei/E*), in which E*, a universal parameter for this system, is the average energy per particle, and expresses through the Boltzmann’s constant k (1.378 ergs/centigrade) the “temperature” T of the system T = E*/k.