Thermodynamic uncertainty relations for bosonic Otto engines

Area of Science:

• Quantum Thermodynamics
• Statistical Mechanics
• Quantum Optics

Background:

• Investigating quantum heat engines is crucial for understanding energy conversion at the quantum level.
• The Otto cycle provides a fundamental thermodynamic cycle for theoretical and experimental studies.
• Bosonic systems offer unique properties for exploring quantum effects in thermodynamics.

Purpose of the Study:

• To analyze the thermodynamic performance of two-mode bosonic engines operating in an Otto cycle.
• To derive exact expressions for work and heat fluctuations and their interdependence with efficiency.
• To establish thermodynamic uncertainty relations for quantum Otto engines.

Main Methods:

• Utilizing a two-mode bosonic system with a tunable unitary bilinear interaction for frequency conversion.
• Implementing an Otto cycle involving relaxation to two baths at different temperatures.
• Applying a two-point-measurement approach to calculate joint probabilities of stochastic work and heat.

Main Results:

• Exact expressions for work and heat fluctuations were derived.
• Identities demonstrating the interdependence of average work, fluctuations, and efficiency were established.
• Novel thermodynamic uncertainty relations linking signal-to-noise ratios of work/heat to entropy production were presented.

Conclusions:

• The study provides a comprehensive framework for analyzing quantum Otto engines with bosonic systems.
• The derived thermodynamic uncertainty relations offer new insights into the fundamental limits of quantum energy conversion.
• The methodology can be extended to analyze quantum Otto engines with different unitary strokes.