Dependence of efficiency on the nonlinear nature of a nanomachine

We establish the power output and efficiency of a single-particle nanomachine whose characteristic component is a nonlinear potential U(r) |r|α. We do so by considering multi-temperature "elliptic" and Carnot-like cycles. In both protocols we verify the linear case α=2 corresponds to a threshold situation. In the former, it establishes the transition from a machine behavior - wherefrom we can extract work - to a refrigerator performance. Last but not least, a closer look at the isentropic lines of these systems sets clear parameter value limitations to the definition of a Carnot cycle using such type of mechanical system. An observation that goes beyond standard thermodynamic conditions, where the existence of a Carnot cycle must be material independent.