Higher-order Efficiency Bound and Its Application to Nonlinear Nano-thermoelectrics

TL;DR

This paper derives a new upper bound on the efficiency of steady-state heat engines that accounts for higher-order fluctuations, providing deeper insights into the power-efficiency tradeoff in nonlinear thermoelectric systems.

Contribution

It introduces a higher-order efficiency bound that is tighter than existing bounds and applicable to nonlinear nanoscale heat engines, revealing the role of higher-order fluctuations.

Findings

The higher-order bound is tighter than the thermodynamic uncertainty relation bound.

The bound is exactly achieved under the tight coupling condition.

Nonlinearity enhances the power-efficiency tradeoff in nanoscale engines.

Abstract

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.