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Published on: December 4, 2017
Probability distribution of work done on a two-level system during a nonequilibrium isothermal process
Petr Chvosta1, Peter Reineker, Michael Schulz
1Department of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University, V Holesovickách 2, CZ-180 00 Prague, Czech Republic. chvosta@kmf.troja.mff.cuni.cz
Summary
We calculated the work done on a two-level system, finding its probability distribution. The study reveals how driving speed affects work, with slow driving matching reversible work and nonequilibrium showing deviations.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Thermodynamics
Background:
- Understanding work fluctuations in driven quantum systems is crucial for quantum thermodynamics.
- Previous studies often relied on approximations for complex systems.
Purpose of the Study:
- To exactly calculate the probability density of work done on a time-dependent two-level system.
- To analyze the influence of driving protocols on work distribution and thermodynamics.
Main Methods:
- Exact calculation of probability density for work done on a two-level system.
- Derivation of an evolution equation for the characteristic function of work.
- Analysis of work distribution under different driving rates.
Main Results:
- The work distribution is controlled by the ratio of driving and internal dynamics timescales.
- Identified sample paths violating the second law of thermodynamics.
- In the slow driving limit, work distribution approaches reversible work.
Conclusions:
- The exact calculation provides a benchmark for quantum thermodynamic studies.
- Driving protocols significantly impact work fluctuations and thermodynamic consistency.
- Deviations from reversible work are prominent in the strongly nonequilibrium regime.
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