  Odd materials feature antisymmetric response to perturbations. This anomalous
property can stem from the nonequilibrium activity of their components, which
is sustained by an external energy supply. These materials open the door to
designing innovative engines which extract work by applying cyclic
deformations, without any equivalent in equilibrium. Here, we reveal that the
efficiency of such energy conversion, from local activity to macroscopic work,
can be arbitrarily close to unity when the cycles of deformation are properly
designed. We illustrate these principles in some canonical viscoelastic
materials, which leads us to identify strategies for optimizing power and
efficiency according to material properties, and to delineate guidelines for
the design of more complex odd engines.
