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Distribution of work in isothermal nonequilibrium processes
1II. Institut für Theoretische Physik, Universität Stuttgart, D-70550 Stuttgart, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
The work distribution for driven diffusive systems is Gaussian for slow driving. However, exact solutions reveal nonanalytic behavior in mean and variance, indicating limitations of approximations.
Area of Science:
- Statistical physics
- Non-equilibrium systems
- Thermodynamics
Background:
- Understanding the behavior of systems driven by external forces is crucial in statistical physics.
- The distribution of work done on a system provides insights into its thermodynamic properties.
Purpose of the Study:
- To investigate the work distribution for diffusive motion in an externally driven potential.
- To analyze the validity of approximations for slow but finite driving rates.
Main Methods:
- Utilized projection method techniques.
- Exploited a small parameter related to the switching rate between system states.
- Derived an exact solution for a simple model system.
Main Results:
- The work distribution is shown to be Gaussian for slow but finite driving.
- The exact solution reveals nonanalytic behavior in the mean and variance.
- Approximations based on slow driving may fail in higher orders.
Conclusions:
- The Gaussian approximation for work distribution is valid under specific conditions (slow driving).
- Nonanalytic behavior in exact solutions highlights the limitations of theoretical approximations.
- Further investigation is needed for higher-order corrections in driven systems.