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

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.

arXiv comment10 pages, 6 figures

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Cited by in corpus (7)

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• Optimal thermodynamic uncertainty relation in Markov jump processes
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• Bounds on fluctuations for ensembles of quantum thermal machines
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