  Partly driven by the need to deal with these objections explicitly probabilistic notions began to be introduced into the theory by Maxwell and Boltzmann. Both realized that equilibrium values for quantities could be calculated by imposing a probability distribution over the microscopic dynamical states compatible with the constraints placed on the system, and identifying the observed macroscopic values with averages over quantities definable from the microscopic states using that probability distribution. But what was the physical justification for this procedure?