  The true import of Boltzmann's results is rather that they provide a generalization of the entropy concept to non-equilibrium states, and a claim that this non-equilibrium entropy \(-kH\) increases monotonically as the isolated gas evolves from non-equilibrium towards an equilibrium state. The relationship with the second law is, therefore, indirect. On the one hand, Boltzmann proves much more than was required, since the second law does not speak of non-equilibrium entropy, nor of monotonic increase; on the other hand it proves also less, since Boltzmann does not consider more general adiabatic processes.