标题： 大偏差的线性逼近：三次扩散检验 显示英文标题

标题： Linear approximations of large deviations: Cubic diffusion test

摘要： 我们提出一种方法，用于近似扩散过程的时间积分可观测量的大偏差率函数，在统计物理中用于表征非平衡系统的涨落。 该方法基于对与所考虑过程和可观测量的大偏差相关联的有效过程进行线性化，并针对一个涉及三次漂移的简单一维非线性扩散模型进行了测试。 结果表明，线性近似与精确率函数相比表现良好，特别是在大涨落区域，其准确性与线性化过程在空间中的定位方式有关。 提出了对未来工作的扩展和应用到更复杂扩散模型的建议。 显示英文摘要

摘要： 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.