Precision bound and optimal control in periodically modulated continuous quantum thermal machines.

Area of Science:

• Quantum thermodynamics
• Statistical mechanics
• Condensed matter physics

Background:

• Periodically modulated quantum thermal machines offer tunable control over thermodynamic processes.
• Understanding fluctuations is key to optimizing the performance and reliability of these machines.

Purpose of the Study:

• To develop a generic theory for fluctuations in periodically modulated continuous quantum thermal machines.
• To investigate the validity and behavior of thermodynamic uncertainty relations (TUR) under various modulation schemes.
• To analyze bounds on efficiency fluctuations for quantum heat engines and refrigerators.

Main Methods:

• Application of the Floquet formalism to analyze quantum thermal machines.
• Development of a generic theoretical framework for modulated machines.
• Specific analysis of sinusoidal, optimal, and circular modulation protocols.
• Numerical analysis to explore TUR signatures and efficiency bounds.

Main Results:

• The thermodynamic uncertainty relations (TUR) are shown to hold universally for all considered modulations.
• For sinusoidal modulation, the TUR ratio is minimized at the engine-refrigerator transition point.
• A chopped random basis optimization protocol maintains a low TUR ratio across a broad frequency range.
• Numerical results indicate that TUR can signal the heat engine to refrigerator transition in generic schemes.
• Efficiency fluctuations are bounded from above for refrigerators and from below for engines.

Conclusions:

• Modulation schemes play a critical role in determining the fluctuation properties of quantum thermal machines.
• The findings provide insights into optimizing quantum thermal devices by controlling modulation strategies.
• This work highlights the interplay between theoretical frameworks and practical design considerations for quantum thermal machines.