Higher-order efficiency bound and its application to nonlinear nanothermoelectrics

Area of Science:

• Thermodynamics
• Nanotechnology
• Statistical Mechanics

Background:

• Heat engines face a fundamental tradeoff between power output and efficiency.
• Existing efficiency bounds, like those from the thermodynamic uncertainty relation, may not fully capture nonlinear behaviors.

Purpose of the Study:

• To derive a novel upper bound on the efficiency of steady-state heat engines.
• To investigate the role of higher-order power fluctuations in the power-efficiency tradeoff.
• To demonstrate the improved accuracy of the new bound in nonlinear regimes.

Main Methods:

• Derivation of a new thermodynamic efficiency bound incorporating higher-order power fluctuations.
• Analysis of a prototypical nonlinear nanostructured thermoelectric engine model.
• Comparison of the new bound with the bound derived from the thermodynamic uncertainty relation.

Main Results:

• A tighter upper bound on heat engine efficiency was derived, including higher-order power fluctuations.
• The new bound proved more accurate than existing bounds in the nonlinear regime.
• The higher-order bound was found to be exactly achieved under tight coupling conditions.
• Nonlinearity was confirmed to enhance the power-efficiency tradeoff.

Conclusions:

• Higher-order power fluctuations provide crucial information for understanding thermodynamic efficiency in nonlinear systems.
• The derived bound offers a more precise prediction of the power-efficiency tradeoff in nanoscale engines.
• This work has implications for the design and optimization of various nanoscale heat engines.