  In an important work (listed in the bibliography), P. and T. Ehrenfest also offered a reading of the Boltzmann equation of approach to equilibrium that avoided recurrence objections. Here the solution of the equation was taken to describe not “the overwhelmingly probable evolution” of a system, but, instead, the sequence of states that would be found overwhelmingly dominant at different times in a collection of systems all started in the same non-equilibrium condition. Even if each individual system approximately recurred to its initial conditions, this “concentration curve” could still show monotonic change toward equilibrium from an initial non-equilibrium condition.