Boltzmanns equation provides a microscopic model for the evolution of dilute classical gases. A fundamental problem in mathematical physics is to rigorously derive Boltzmanns equation starting from Newtons laws. In the 1970s, Oscar Lanford provided such a derivation, for the hard sphere interaction, on a small time interval. One of the subtleties of Lanfords original proof was that the strength of convergence proven at positive times was much weaker than that which had to be assumed at the initial time, which is at odds with the idea of propagation of chaos. Several authors have addressed this situation with various notions of strong one-sided chaos, which is the true property which is propagated by the dynamics. We provide a new approach to the problem based on duality and the evolution of observables; the observables encode the detailed interaction and allow us to define a new notion of strong one-sided chaos.
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