Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound

Area of Science:

• Quantum thermodynamics
• Statistical mechanics
• Information theory

Background:

• A key question in thermodynamics is whether heat engines can achieve maximum theoretical efficiency (Carnot efficiency) at finite power.
• Previous studies often assumed Markovian dynamics, limiting their applicability.

Purpose of the Study:

• To rigorously investigate the trade-off between power and efficiency in quantum heat engines.
• To establish a general theoretical framework applicable to both Markovian and non-Markovian quantum heat engines.

Main Methods:

• Utilizing the Lieb-Robinson bound to analyze the impact of local operations on quantum systems.
• Applying quantum information geometry to derive bounds on thermodynamic efficiency.
• Developing a general trade-off inequality for cyclic quantum heat engine processes.

Main Results:

• A rigorous proof of a general trade-off inequality relating thermodynamic efficiency and the time interval of a cyclic quantum heat engine.
• Demonstrated that finite power operation precludes achieving Carnot efficiency in quantum heat engines.
• The derived constraint is valid for engines with non-Markovian dynamics, a significant advancement over prior work.

Conclusions:

• The study definitively excludes the possibility of achieving Carnot efficiency at finite power for quantum heat engines.
• The findings have broad implications for the design and understanding of quantum thermal devices, particularly those operating under complex, non-Markovian conditions.