Geometric Formulation of Power-Efficiency Bounds in Carnot-like Engines

TL;DR

This paper introduces a geometric optimization framework to analyze power-efficiency bounds in Carnot-like engines, providing exact and closed-form results for various dissipation models.

Contribution

It formulates power-efficiency constraints as a geometric problem and derives exact bounds for power-law dissipation models, including maximum power.

Findings

Efficiency contours are straight lines in the dissipation plane.

The power-efficiency frontier can be exactly characterized within the model.

Closed-form constraints are obtained for different dissipation exponents.

Abstract

We formulate the power-efficiency constraint of Carnot-like heat engines as a geometric optimization problem in the plane of normalized branch dissipations. Efficiency contours are straight lines in this plane, so maximizing efficiency at fixed power reduces to bounding the slope of an admissible line. We apply this framework to branch-resolved power-law dissipation, where the irreversible loss on each isothermal branch decays with the branch duration with a common exponent rather than following the standard inverse-time law. After optimizing over the dissipation-asymmetry parameter, the fixed-power attainable set becomes a two-dimensional region, and the resulting slope-bound problem reduces to linear programming. The framework yields the exact power-efficiency frontier within this model and gives closed-form constraints for representative dissipation exponents, including the maximum-power limit.