Geometric Heat Engines Featuring Power that Grows with Efficiency

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Non-equilibrium Physics

Background:

• Classical thermodynamics defines limits on heat engine efficiency (Carnot limit) but not on output power or its dependence on cycle time.
• Understanding heat engine performance under non-equilibrium conditions and fast driving is crucial for developing advanced energy technologies.

Purpose of the Study:

• To develop a geometrical framework for analyzing heat engine power and efficiency as functions of cycle time.
• To design protocols that achieve maximal power and efficiency in the fast driving limit.
• To investigate the attainability of Carnot efficiency at non-zero power output.

Main Methods:

• Development of a geometrical description for heat engine power and efficiency.
• Application of this geometrical framework to a class of heat engine models.
• Design and analysis of engine protocols under varying cycle times.

Main Results:

• A geometrical method was established to describe heat engine power and efficiency concerning cycle time.
• Protocols were designed to achieve maximal power and efficiency at the fast driving limit.
• It was proven that exact Carnot efficiency cannot be reached at non-zero power output.

Conclusions:

• The geometrical approach provides a powerful tool for optimizing heat engine performance.
• Maximal power and efficiency can be simultaneously achieved in the fast driving limit.
• The findings clarify fundamental limitations of heat engines operating out of equilibrium.