  We consider the kinetic theory of dilute gases in the Boltzmann--Grad limit.
We propose a new perspective based on a large deviation estimate for the
probability of the empirical distribution dynamics. Assuming Boltzmann
molecular chaos hypothesis (Stosszahlansatz), we derive a large deviation rate
function, or action, that describes the stochastic process for the empirical
distribution. The quasipotential for this action is the negative of the
entropy, as should be expected. While the Boltzmann equation appears as the
most probable evolution, corresponding to a law of large numbers, the action
describes a genuine reversible stochastic process for the empirical
distribution, in agreement with the microscopic reversibility. As a
consequence, this large deviation perspective gives the expected meaning to the
Boltzmann equation and explains its irreversibility as the natural consequence
of limiting the physical description to the most probable evolution. More
interestingly, it also quantifies the probability of any dynamical evolution
departing from solutions of the Boltzmann equation. This picture is fully
compatible with the heuristic classical view of irreversibility, but makes it
much more precise in various ways. We also explain that this large deviation
action provides a natural gradient structure for the Boltzmann equation.
