Thermodynamic Uncertainty Relation in Slowly Driven Quantum Heat Engines

Area of Science:

• Thermodynamics
• Quantum Thermodynamics
• Statistical Mechanics

Background:

• Thermodynamic uncertainty relations (TURs) establish a fundamental trade-off between precision (noise-to-signal ratio) and entropy production.
• For steady-state heat engines, TURs impose limits on efficiency based on power output and fluctuations.

Purpose of the Study:

• To investigate TURs for heat engines operating in the periodic slow-driving regime.
• To determine if less restrictive bounds exist for non-steady-state engines.
• To incorporate the impact of quantum fluctuations on engine performance.

Main Methods:

• Analysis of thermodynamic uncertainty relations in the periodic slow-driving regime.
• Derivation of a new TUR applicable to this regime.
• Modeling a single-ion heat engine to illustrate the theoretical findings.

Main Results:

• An alternative TUR is identified for periodically driven heat engines.
• This new TUR is less restrictive than steady-state bounds, permitting high efficiency with low power fluctuations.
• Quantum fluctuations are shown to reduce engine efficiency relative to average power and reliability.

Conclusions:

• Periodically driven heat engines can operate closer to reversibility than previously thought.
• The derived TUR provides a more nuanced understanding of efficiency limits in non-equilibrium systems.
• The findings have implications for designing and optimizing quantum heat engines.