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Nonequilibrium Lyapunov function and a fluctuation relation for stochastic systems: Poisson-representation approach
1Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.
Summary
This study introduces a statistical physics framework to analyze nonlinear nonequilibrium stochastic processes. The research develops a method to derive fluctuation relations and identifies a nonequilibrium free energy that acts as a Lyapunov function.
Area of Science:
- Statistical physics
- Nonlinear dynamics
- Stochastic processes
Background:
- Nonlinear nonequilibrium stochastic processes are fundamental in many scientific fields.
- Modeling these systems often involves complex mathematical approaches like the chemical master equation.
- Understanding their behavior, especially under control, requires advanced theoretical frameworks.
Purpose of the Study:
- To develop a statistical physics framework for nonlinear nonequilibrium stochastic processes in the weak-noise limit.
- To derive an integral fluctuation relation for such systems under feedback control.
- To identify and utilize a nonequilibrium free energy as a Lyapunov function.
Main Methods:
- Utilizing the Poisson-representation approach.
- Applying the large-deviation principle to solve the chemical master equation.
- Deriving integral fluctuation relations using the concept of nonequilibrium free energy.
Main Results:
- A method to solve the master equation in the weak-noise limit.
- An integral fluctuation relation for nonlinear nonequilibrium systems under feedback control.
- Identification of a nonequilibrium free energy that functions as a monotonic Lyapunov function.
Conclusions:
- The developed framework provides a robust method for analyzing complex stochastic systems.
- The identified Lyapunov function offers insights into system stability and behavior.
- The Poisson-representation technique is applicable to various biophysical processes.
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