Thermodynamic uncertainty relation for quantum work distribution: Exact case study for a perturbed oscillator

Area of Science:

• Quantum thermodynamics
• Nonequilibrium statistical mechanics
• Mesoscopic systems

Background:

• General relations in nonequilibrium mesoscopic systems are under investigation.
• The thermodynamic uncertainty relation (TUR) bounds current precision by entropy production.
• Work fluctuation is significant but TUR applicability requires specific conditions.

Purpose of the Study:

• To analytically demonstrate TUR for work in a quantum harmonic oscillator.
• To investigate the impact of noncommutativity on thermodynamic precision.
• To explore the experimental feasibility of these findings.

Main Methods:

• Analytical derivation of the thermodynamic uncertainty relation.
• Analysis of a quantum harmonic oscillator model interacting with multiple reservoirs.
• Investigation in the full quantum regime.

Main Results:

• The thermodynamic uncertainty relation (TUR) is shown to hold for work performed on a quantum harmonic oscillator.
• The effect of noncommutativity on thermodynamic precision is quantified.
• The study provides insights into the experimental accessibility of these quantum thermodynamic relations.

Conclusions:

• The TUR is a valid and general principle for work fluctuations in driven quantum systems.
• Noncommutativity plays a crucial role in determining thermodynamic precision.
• The findings pave the way for experimental verification in quantum systems.