  It is known that an engine with ideal efficiency ($\eta =1$ for a chemical
engine and $e = e_{\rm Carnot}$ for a thermal one) has zero power because a
reversible cycle takes an infinite time. However, at least from a theoretical
point of view, it is possible to conceive (irreversible) engines with nonzero
power that can reach ideal efficiency. Here this is achieved by replacing the
usual linear transport law by a sublinear one and taking the step-function
limit for the particle current (chemical engine) or heat current (thermal
engine) versus the applied force. It is shown that in taking this limit exact
thermodynamic inequalities relating the currents to the entropy production are
not violated.
