Periodically Driven Quantum Thermal Machines from Warming up to Limit Cycle.

Area of Science:

• Quantum Thermodynamics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Current theories on periodically driven quantum thermal machines (PD-QTMs) primarily focus on the accessible limit-cycle operation stage.
• Experimental verification of PD-QTMs is challenging due to the inaccessibility of the limit-cycle regime.

Purpose of the Study:

• To develop a general thermodynamic framework for PD-QTMs applicable both before and during the limit-cycle stage.
• To provide a more complete description of the first law of thermodynamics for PD-QTMs, especially under strong coupling conditions.

Main Methods:

• Developed a theoretical framework analyzing PD-QTM performance beyond the limit-cycle stage.
• Incorporated ensemble-averaged breakdown of periodicity.
• Utilized conventional thermodynamic expressions for work and heat.

Main Results:

• Identified a new contribution to the first law of thermodynamics for PD-QTMs.
• This contribution vanishes in the limit-cycle phase only under weak system-bath couplings.
• The contribution is substantial at strong couplings, significantly impacting thermodynamic efficiency.

Conclusions:

• The new framework offers a comprehensive understanding of PD-QTMs from initiation to steady-state operation.
• Provides crucial insights into quantum thermodynamics, particularly for systems with strong coupling.
• Highlights the importance of considering pre-limit-cycle dynamics and coupling strengths for accurate performance analysis.