  It was Boltzmann who first proposed a kind of “cosmological” solution to the problem. As noted above he suggested a universe overall close to equilibrium with “small” sub-regions in fluctuations away from that state. In such a sub-region we would find a world far from equilibrium. Introducing the familiar time-symmetric probabilistic assumptions, it becomes likely that in such a region one finds states of lower entropy in one time direction and states of higher entropy in the other. Then finish the solution by introducing the other Boltzmann suggestion that what we mean by the future direction of time is fixed as that direction of time in which entropy is increasing.