  This rebuttal of Loschmidt is far from satisfactory. Any reasonable probability assignment to gas states is presumably invariant under the velocity reversal of the molecules. If an initial state leading to an increase of \(H\) is to be ignored on account of its small probability, one ought to assume the same for the state from which it was constructed by velocity reversal. In other words, any non-equilibrium state would have to be ignored. But that in effect saves the H-theorem by restricting it to those cases where it is trivially true, i.e., where \(H\) is constant.