  For perturbative scalar field theories, the late-time-limit of the
out-of-time-ordered correlation function that measures (quantum) chaos is shown
to be equal to a Boltzmann-type kinetic equation that measures the total gross
(instead of net) particle exchange between phase space cells, weighted by a
function of energy. This derivation gives a concrete form to numerous attempts
to derive chaotic many-body dynamics from ad hoc kinetic equations. A period of
exponential growth in the total gross exchange determines the Lyapunov exponent
of the chaotic system. Physically, the exponential growth is a front
propagating into an unstable state in phase space. As in conventional Boltzmann
transport, which follows from the dynamics of the net particle number density
exchange, the kernel of this kinetic integral equation is also set by the
2-to-2 scattering rate. This provides a mathematically precise statement of the
known fact that in dilute weakly coupled gases transport and scrambling (or
ergodicity) are controlled by the same physics.
