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Work fluctuations for Bose particles in grand canonical initial states
Juyeon Yi1, Yong Woon Kim, Peter Talkner
1Department of Physics, Pusan National University, Busan 609-735, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
Investigating work fluctuations in trapped bosons reveals that the exponentiated work average may diverge under specific conditions. The probability distribution function of work signals this divergence, showing asymmetric behavior at low temperatures and Gaussian-like behavior at high temperatures.
Area of Science:
- Quantum statistical mechanics
- Thermodynamics of small systems
Background:
- Bosons in harmonic traps are a key model in quantum statistical mechanics.
- Fluctuations in work performed during non-equilibrium processes are crucial for understanding thermodynamics.
- The Crooks relation and Jarzynski equality connect equilibrium free energy differences to non-equilibrium work statistics.
Purpose of the Study:
- To investigate the fluctuations of work performed on bosons in a harmonic trap during adiabatic changes in trap curvature.
- To analyze how the probability distribution function (PDF) of work signals the divergence of the exponentiated work average (EWA).
- To explore the relationship between work PDF properties, EWA convergence, and the existence of hypothetical equilibrium states.
Main Methods:
- Adiabatic change of harmonic trap curvature for bosons.
- Analysis of work fluctuations and their probability distribution function (PDF).
- Application of concepts from the Crooks relation and Jarzynski equality.
Main Results:
- The exponentiated work average (EWA) can diverge depending on reservoir conditions (temperature, chemical potential) and trap widening.
- The work PDF exhibits high asymmetry with an exponential tail at low temperatures.
- At high temperatures, the work PDF approaches a symmetric, Gaussian-like form.
Conclusions:
- The observed properties of the work PDF are directly linked to the convergence of the EWA.
- The study provides insights into the conditions under which thermodynamic potentials, as defined by the Crooks relation and Jarzynski equality, are well-defined.
- Understanding work fluctuations is essential for characterizing non-equilibrium processes in quantum systems.
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