  We show that the extension of Casimir-like forces to fluctuating fluids
driven out of equilibrium can exhibit two interrelated phenomena forbidden at
equilibrium: self-forces can be induced on single asymmetric objects and the
action--reaction principle between two objects can be violated. These effects
originate in asymmetric restrictions imposed by the objects' boundaries on the
fluid's fluctuations. They are not ruled out by the second law of
thermodynamics since the fluid is in a nonequilibrium state. Considering a
simple reaction--diffusion model for the fluid, we explicitly calculate the
self-force induced on a deformed circle. We also show that the action--reaction
principle does not apply for the internal Casimir forces exerting between a
circle and a plate. Their sum, instead of vanishing, provides the self-force on
the circle-plate assembly.
