  Arguments based on symmetry and thermodynamics may suggest the existence of a
ratchet-like lateral Casimir force between two plates at different temperatures
and with broken inversion symmetry. We find that this is not sufficient, and at
least one plate must be made of nonreciprocal material. This setup operates as
a heat engine by transforming heat radiation into mechanical force. Although
the ratio of the lateral force to heat transfer in the near field regime
diverges inversely with the plates separation, $d$, an Onsager symmetry, which
we extend to nonreciprocal plates, limits the engine efficiency to the Carnot
value $\eta_c$. The optimal velocity of operation in the far field is of the
order of $c\eta_c$, where $c$ is the speed of light. In the near field regime,
this velocity can be reduced to the order of $\bar\omega d \eta_c$, where
$\bar\omega$ is a typical material frequency.
