  Power and efficiency of heat engines are two conflicting objectives, and a
tight efficiency bound is expected to give insights on the fundamental
properties of the power-efficiency tradeoff. Here we derive an upper bound on
the efficiency of steady-state heat engines, which incorporates higher-order
fluctuations of the power. In a prototypical model of nonlinear nanostructured
thermoelectrics, we show that the obtained bound is tighter than a
well-established efficiency bound based on the thermodynamic uncertainty
relation, demonstrating that the higher-order terms have rich information about
the thermodynamic efficiency in the nonlinear regime. In particular, we find
that the higher-order bound is exactly achieved if the tight coupling condition
is satisfied. The obtained bound gives a consistent prediction with the
observation that nonlinearity enhances the power-efficiency tradeoff, and would
also be useful for various nanoscale engines.
