Deriving the Boltzmann Energy Distribution

Deriving the Boltzmann energy distribution is commonly effected through maximizing distinguishable arrangements subject to constraints. In this process, the constraints are accounted for using the Lagrange method of undetermined multipliers. Unfortunately, many students lack the mathematical background necessary to properly appreciate the Lagrange method. It is here shown that maximizing distinguishable arrangements subject to constraints can be readily effected—although admittedly less elegantly—without involving the Lagrange method.