Boltzmann distribution [SEP] named after
energy difference:
The Boltzmann distribution is named after Ludwig Boltzmann who first formulated it in 1868 during his studies of the statistical mechanics of gases in thermal equilibrium. Boltzmann's statistical work is borne out in his paper “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium"
The distribution was later investigated extensively, in its modern generic form, by Josiah Willard Gibbs in 1902.
The generalized Boltzmann distribution is a sufficient and necessary condition for the
of the motion called heat", Clausius for the first time clearly states that heat is the average kinetic energy of molecules. This interested Maxwell, who in 1859 derived the momentum distribution later named after him. Boltzmann subsequently generalized his distribution for the case of gases in external fields.
Boltzmann is perhaps the most significant contributor to kinetic theory, as he introduced many of the fundamental concepts in the theory. Besides the Maxwell–Boltzmann distribution mentioned above, he also associated the kinetic energy of particles with their degrees of freedom