Efficiency at optimal performance: A unified perspective based on coupled autonomous thermal machines.

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Non-equilibrium systems

Background:

• The efficiency at maximum power (EMP) is a key metric for heat engines operating out of equilibrium.
• Previous studies primarily focused on two-reservoir models, limiting understanding of more complex systems.
• Linear-irreversible thermodynamics provides a framework for analyzing such systems.

Purpose of the Study:

• To investigate the efficiency at maximum power (EMP) of coupled autonomous thermal machines with three heat reservoirs.
• To establish an analogy between the EMP of three-reservoir systems and established two-reservoir models.
• To explore the temperature dependence and universal properties of EMP in these coupled systems.

Main Methods:

• Global linear-irreversible thermodynamic description of coupled autonomous thermal machines.
• Analysis of the efficiency at maximum power (EMP) under varying reservoir temperatures.
• Mathematical derivation and comparison with existing models in the literature.

Main Results:

• The EMP of three-reservoir systems shows a form analogous to two-reservoir systems.
• Temperature dependence of EMP is determined by the ratio of hot and cold reservoir temperatures when the intermediate temperature is an algebraic mean.
• Universal properties of EMP near equilibrium are explained by symmetric means, with a predicted second-order coefficient of 6/49 for broken time-reversal symmetry.

Conclusions:

• Coupled thermal machines with three reservoirs can achieve EMP characteristics similar to simpler two-reservoir models.
• The study unifies various EMP expressions through the concept of algebraic means.
• New insights into the universal behavior of EMP are provided, particularly for systems with broken time-reversal symmetry.