At the end of 19th century there was a lively discussion about the nature of the second law of thermodynamics, and its relation to Hamiltonian dynamics. Boltzmann developed a position that the second law is statistical in nature, "ordered" states are less probable, and the entropy is "highly unlikely" to decrease. As a confirmation he offered the H-theorem, a claim that entropy increases in a nearly ideal gas of particles.
But first Loschmidt objected that Boltzmann's "proof" of the H-theorem had a gap in neglecting correlations due to collisions, and in 1896 Zermelo disputed all of the above. He pointed out that statistical equations of Hamiltonian dynamics (Liouville equations) are just as time reversible as equations for individual particles, and therefore so are the equations for probabilities. Hence entropy is not "likely" to decrease or increase, it has to stay constant (up to deviations due to finite if large number of particles, so-called thermal fluctuations). As an illustration Zermelo brought up the Poincare recurrence theorem, which says that every state of a system nearly recurs infinitely many times in its evolution. He concluded that the second law is mathematically inconsistent with Hamiltonian dynamics, and no amount of probability theory can fix that. Poincare expressed the same opinion earlier (1889).
It is interesting that contemporaries thought that Boltzmann won the debate, but Boltzmann felt backed into a corner and "lost faith in himself" (according to Popper's Unended Quest). His response was the fluctuation hypothesis that our vicinity is a giant fluke in the universe, where the second law happens to hold. Zermelo in his turn suggested that the second law might be a selection rule on initial states rather than a "law of nature", but commented that such fix contradicts the "spirit of mechanics", and would not "satisfy anybody for long". Nonetheless, according to Wikipedia "much effort in the field is attempting to understand why the initial conditions early in the universe were those of low entropy, as this is seen as the origin of the second law". How selection of initial states resolves the issue of the entropy staying constant I am not sure. Soon after 1896 the attention of physicists shifted to relativity and quantum mechanics, and the second law dropped out of sight.
Was this debate picked up by others later? If so who advocated what position and how? Who was closer to the truth from the modern point of view, Zermelo or Boltzmann?
EDIT: Here is a modern exposition of the ideas of Ehrenfests and Mark Kac mentioned in the Alexandre's answer. It turns out that the missing ingredient was coarse-graining (macroscopic averaging) introduced by Gibbs in 1902 in a direct follow-up to the debate. Time reversible microscopic systems have evolutions in which coarse-grained entropy appears to grow for astronomically long periods of time, in the spirit of Boltzmann. Of course, they also have evolutions, where the opposite happens. We only observe the former but not the latter, so there is a selection of initial states suggested by Zermelo.
It seems that they were both half right, but lacked the idea of coarse-graining which reconciles their positions. The nature of selection is apparently still unclear and is traced to low entropy "early in the universe", which attracts "much effort in the field", see details here.
