  We show that the quasiparticle kinetic theory for quantum and classical
Calogero models reduces to the free-streaming Boltzmann equation. We reconcile
this simple emergent behaviour with the strongly interacting character of the
model by developing a Bethe-Lax correspondence in the classical case. This
demonstrates explicitly that the freely propagating degrees of freedom are not
bare particles, but rather quasiparticles corresponding to eigenvectors of the
Lax matrix. We apply the resulting kinetic theory to classical Calogero
particles in external trapping potentials and find excellent agreement with
numerical simulations in all cases, both for harmonic traps that preserve
integrability and exhibit perfect revivals, and for anharmonic traps that break
microscopic integrability. Our framework also yields a simple description of
multi-soliton solutions in a harmonic trap, with solitons corresponding to
sharp peaks in the quasiparticle density. Extensions to quantum systems of
Calogero particles are discussed.
