Universality of efficiency at unified trade-off optimization

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Physical Chemistry

Background:

• Heat engines are crucial for energy conversion.
• Optimizing heat engine efficiency involves balancing useful energy output with energy loss.
• The maximum Ω (Omega) criterion offers a unified approach to this optimization.

Purpose of the Study:

• To calculate the efficiency of heat engines at the maximum Ω (Omega) criterion.
• To determine the universality of efficiency coefficients under specific conditions.
• To extend the findings to ecological optimization criteria.

Main Methods:

• Thermodynamic analysis of heat engines operating between two reservoirs.
• Calculation of efficiency under strong coupling and symmetry conditions.
• Mathematical derivation of linear and quadratic coefficients.

Main Results:

• The linear coefficient of efficiency at maximum Ω (Omega) is 3/4.
• The quadratic coefficient of efficiency at maximum Ω (Omega) is 1/32.
• These coefficients are universal for heat engines under strong coupling and symmetry.

Conclusions:

• The derived efficiency coefficients are universally applicable under the specified conditions.
• The results are also valid for the ecological optimization criterion.
• This provides a unified understanding of heat engine optimization.