Attainability of Carnot efficiency with autonomous engines

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Non-equilibrium Systems

Background:

• Autonomous engines operate with a finite chemical potential difference.
• Understanding the theoretical limits of engine efficiency is crucial for energy conversion.
• Carnot efficiency represents the theoretical maximum for heat engines.

Purpose of the Study:

• To investigate the maximum achievable efficiency of autonomous engines.
• To determine the conditions under which autonomous engines can attain Carnot efficiency.
• To identify the role of singularities in engine performance.

Main Methods:

• Theoretical analysis of autonomous engine models.
• Investigation of systems with finite chemical potential differences.
• Examination of single particle transport phenomena.
• Analysis under the thermodynamic limit.

Main Results:

• Autonomous engines cannot reach Carnot efficiency without a specific type of singularity.
• A particular singularity is identified as necessary for achieving maximum efficiency.
• Single particle transports and the thermodynamic limit are shown to realize this singularity.
• Concrete setups demonstrate that these singularity conditions lead to Carnot efficiency.

Conclusions:

• The presence of a singularity is crucial for autonomous engines to achieve maximum efficiency.
• The identified singularity, realized through specific transport mechanisms or limits, enables Carnot efficiency.
• This work highlights the fundamental role of singularities in the thermodynamics of autonomous engines.