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Dynamical large deviations of linear diffusions
Johan du Buisson1, Hugo Touchette2
1Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch 7600, South Africa.
We studied fluctuations in linear diffusion systems using large deviation theory. Exact results reveal how these fluctuations arise from effective forces or fluctuating currents in nonequilibrium systems.
Area of Science:
- Statistical Physics
- Nonlinear Dynamics
- Stochastic Processes
Background:
- Linear diffusions model physical systems like Brownian motion and electrical circuits with thermal noise.
- Understanding fluctuations is crucial for characterizing nonequilibrium systems.
Purpose of the Study:
- To derive exact results for time-integrated functionals of linear diffusions.
- To analyze fluctuations in nonequilibrium systems using large deviation theory.
Main Methods:
- Application of large deviation theory techniques.
- Derivation of scaled cumulant generating functions and rate functions.
- Analysis of underlying path ensembles and effective processes.
Main Results:
- Exact results for fluctuations of linear and quadratic time-integrated functionals.
- Characterization of fluctuations via linear effective forces or fluctuating currents solving Riccati equations.
- Complete description of fluctuation origins in linear diffusions.
Conclusions:
- The study provides a comprehensive framework for understanding fluctuations in linear diffusions.
- The derived methods and results are applicable to various nonequilibrium physical models.
- Illustrative examples include 2D transverse diffusion and interacting particles in heat baths.
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