 The reader can find this story in many textbooks and in many references cited above. An objection in their spirit (specifically, Loschmidt’s) can also be advanced against Boltzmann’s later view sketched above. Loosely put, because the classical equations of motion are time reversal invariant, nothing in the original explanation necessarily referred to the direction of time (see Hurley 1986). Although we just stated the Boltzmannian account of entropy increase in terms of entropy increasing into the future, the explanation can be turned around and made for the past temporal direction as well. Given a gas in a box that is in a nonequilibrium state, the vast majority of microstates that are antecedents of the dynamical evolution leading to the present macrostate correspond to a macrostate with higher entropy than the present one. Therefore, not only is it highly likely that typical microstates corresponding to a nonequilibrium state will evolve to  higher entropy states, but it is also highly likely that they evolved from higher entropy states.