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Entropy and temperature in finite isolated quantum systems.
Phillip C Burke1, Masudul Haque1,2,3
1Department of Theoretical Physics, Maynooth University, Maynooth, W23 F2H6 Kildare, Ireland.
Physical Review. E
|April 19, 2023
Summary
We compared temperatures from microcanonical entropy and canonical temperature in finite quantum systems. Specific energy window calculations minimize deviations, improving ensemble equivalence understanding.
Area of Science:
- Quantum statistical mechanics
- Thermodynamics of small systems
Background:
- Canonical and microcanonical ensembles are fundamental in statistical mechanics.
- Ensemble equivalence is typically assumed for large systems but breaks down for finite systems.
- Understanding deviations is crucial for quantum thermodynamics.
Purpose of the Study:
- To compare temperatures derived from microcanonical entropy and canonical temperature.
- To quantify ensemble equivalence deviations in finite isolated quantum systems.
- To identify methods for accurate temperature calculation in small quantum systems.
Main Methods:
- Numerical exact diagonalization of quantum systems.
- Calculation of microcanonical entropy using various energy binning strategies.
- Comparison of temperatures derived from different entropy calculations with the canonical temperature.
Main Results:
- Deviations from ensemble equivalence were characterized for finite-size systems.
- Multiple methods for computing microcanonical entropy were evaluated.
- A specific energy window dependence was found to minimize temperature deviations.
Conclusions:
- The choice of energy window significantly impacts temperature calculation from microcanonical entropy.
- Optimal energy window selection can improve the agreement between microcanonical and canonical temperatures.
- This work provides a method to better understand and calculate thermodynamic properties in finite quantum systems.
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