https://doi.org/10.1140/epjb/s10051-025-01108-9
Research - Statistical and Nonlinear Physics
Linear approximations of large deviations: cubic diffusion test
1
Department of Physics, University of Buea, Buea, Cameroon
2
Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa
a
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Received:
1
September
2025
Accepted:
10
December
2025
Published online:
14
January
2026
We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on linearizing the effective process associated with the large deviations of the process and observable considered, and is tested for a simple one-dimensional nonlinear diffusion model involving a cubic drift. The results show that the linear approximation compares well with the exact rate function, especially in the large fluctuation regime, and that its accuracy is related to the way the linearized process localizes in space. Possible extensions and applications to more complex diffusion models are proposed for future work.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
