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Microcanonical work and fluctuation relations for an open system: An exactly solvable model
1Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 16, 2013
Summary
Researchers calculated work probability distributions for a harmonic oscillator interacting with its environment. They verified fluctuation relations and showed ensemble equivalence in the large environment limit.
Area of Science:
- Statistical Mechanics
- Quantum Thermodynamics
- Condensed Matter Physics
Background:
- Understanding work fluctuations in driven quantum systems is crucial for thermodynamics.
- Exact solutions are valuable for validating approximations and exploring fundamental principles.
Purpose of the Study:
- To calculate the probability distribution of work for a precisely solvable model of a system coupled to an environment.
- To investigate the validity of nonequilibrium work and fluctuation relations under various conditions.
Main Methods:
- An exactly solvable model featuring a harmonic oscillator with a time-dependent parameter interacting bilinearly with harmonic environmental oscillators.
- Sampling initial conditions from a microcanonical distribution and driving the system out of equilibrium via a prescribed protocol.
Main Results:
- The study recovers the nonequilibrium work and Crooks's fluctuation relations in the limit of an infinitely large environment (N→∞).
- The microcanonical Crooks relation is confirmed for finite environments.
- Equivalence between canonical and microcanonical ensembles for multitime correlation functions is demonstrated in the infinite environment limit.
Conclusions:
- The findings provide exact results for work distributions and fluctuation relations in open quantum systems.
- The study highlights the importance of the environment's size and initial state distribution in determining thermodynamic relations.
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