Work Fluctuations in Ergotropic Heat Engines

Area of Science:

• Quantum Thermodynamics
• Statistical Mechanics
• Quantum Information

Background:

• Ergotropic heat engines utilize quantum systems to perform work.
• Quantum Otto engines are a key model for studying thermodynamic cycles.
• Ergotropy represents the maximum work extractable via unitary evolution.

Purpose of the Study:

• Investigate work fluctuations in two-stroke quantum Otto engines.
• Analyze ergotropy extraction from quantum systems at different temperatures.
• Examine the role of unitary strokes in work statistics.

Main Methods:

• Derivation of complete work statistics for two qutrits.
• Analysis of optimal unitary strokes (U1, U2, U3).
• Study of thermodynamic uncertainty relations (TURs) and fluctuation theorems.

Main Results:

• Identified three optimal unitary strokes: swap (U1), idle swap (U2), and their composition (U3).
• U1 and U2 are Hermitian, while U3 is non-Hermitian.
• The non-Hermitian transformation U3 violates thermodynamic uncertainty relations derived from detailed fluctuation theorems.

Conclusions:

• The nature of unitary strokes significantly impacts work fluctuations and thermodynamic relations.
• Non-Hermitian operations can lead to violations of established thermodynamic uncertainty bounds.
• Findings offer insights into the fundamental limits of work extraction in quantum engines.