Clausius' above statement interested the Scottish mathematician and physicist James Clerk Maxwell, who in 1859 derived the momentum distribution later named after him. The Austrian physicist Ludwig Boltzmann subsequently generalized this distribution for the case of gases in external fields. In association with Clausius, in 1871, Maxwell formulated a new branch of thermodynamics called statistical thermodynamics, which functions to analyze large numbers of particles at equilibrium, i.e., systems where no changes are occurring, such that only their average properties as temperature T, pressure P, and volume V become important.