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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.02732 |
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| _version_ | 1866909012627292160 |
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| author | Zhai, R. X. |
| author_facet | Zhai, R. X. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Formulation of Power-Efficiency Bounds in Carnot-like Engines Zhai, R. X. Statistical Mechanics 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. |
| title | Geometric Formulation of Power-Efficiency Bounds in Carnot-like Engines |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2605.02732 |