  We have, then, a kind of “transcendental deduction” of the standard probability assigned over microscopic states in the case of equilibrium. Equilibrium is a time-unchanging state. So we demand that the probability measure by which equilibrium quantities are to be calculated be stationary in time as well. If we assume that probability measures assigning non-zero probability to sets of states assigned zero by the usual measure can be ignored, then we can show that the standard probability is the only such time invariant probability under the dynamics that drives the individual systems from one microscopic state to another.