 Boltzmann, Gibbs and many others make the case, although it’s worth bearing in mind that they do so rigorously only in ideal cases and much remains controversial (see above). Still, it strikes many as physically plausible. One could say a lot more, but let’s grant this. Then notice that the first problem of the direction of time is blocked by the Past Hypothesis. One conditionalizes on the uniform distribution given \(M(0)\) and \(M(t)\), not merely \(M(t)\). The constraint at one end of the universe makes the claim that earlier entropy was higher unlikely. If correct, we have an honest-to-goodness reduction of a special science law “the second law of thermodynamics” from the bottom.