  In the limit of short mean free path, relativistic kinetic theory gives rise
to hydrodynamics through a systematically improvable gradient expansion. In the
present work, a systematically improvable expansion in the opposite limit of
large mean free path is considered, describing the dynamics of particles which
are almost, but not quite, non-interacting. This non-hydrodynamic "eremitic"
expansion does not break down for large gradients, and may be useful in
situations where a hydrodynamic treatment is not applicable. As applications,
azimuthal anisotropies at high transverse momentum in Pb+Pb and p+Pb collisions
at $\sqrt{s}=5.02$ TeV are calculated from the first order eremitic expansion
of kinetic theory in the relaxation time approximation.
