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Variational approach to KPZ: Fluctuation theorems and large deviation function for entropy production.
Horacio S Wio1, Miguel A Rodríguez2, Rafael Gallego3
1IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), Universitat de les Illes Balears-CSIC, 07122 Palma de Mallorca, Spain.
This study adapts a path-integral scheme to analyze fluctuation theorems in the unstable Kardar-Parisi-Zhang (KPZ) system. The method allows for detailed and integral fluctuation theorems and entropy production analysis.
Area of Science:
- Statistical physics
- Non-equilibrium systems
Background:
- The Kardar-Parisi-Zhang (KPZ) equation describes driven interfaces and exhibits complex, unstable behavior.
- Standard methods struggle with systems lacking stationary probability distributions.
Purpose of the Study:
- To develop a method for studying fluctuation theorems in unstable systems like the KPZ equation.
- To analyze detailed and integral fluctuation theorems and entropy production.
Main Methods:
- Adaptation of a path-integral scheme.
- Application of a variational approach.
- Analysis of systems without stationary probability distributions.
Main Results:
- A methodology is presented for obtaining detailed and integral fluctuation theorems for the KPZ system.
- The path-integral approach is suitable for unstable systems.
- The method enables the determination of a large deviation function for entropy production.
Conclusions:
- The developed path-integral and variational approach effectively analyzes fluctuation theorems in unstable systems.
- This framework provides insights into non-equilibrium statistical mechanics and entropy production.
- The methodology is extendable to other similar unstable systems.
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