利用分数偏移随机微分方程计算非平衡响应
Computing Nonequilibrium Responses with Score-shifted Stochastic Differential Equations
AI总结：
该研究提出利用含与系统瞬时概率密度score成正比额外漂移的有效物理过程描述受扰动力学，结合score学习算法，解决了传统非平衡线性响应理论无法处理扩散常数变化扰动的问题。
摘要：
利用平衡涨落理解物理系统对外加扰动的响应是线性响应理论的基础，该理论被广泛用于解释实验并揭示微观动力学。对于非平衡系统，仅通过监测共轭可观测量的涨落无法简单解释扰动——还需要额外的动力学信息。围绕非平衡稳态的线性响应理论依赖于路径系综平均，这使得该理论无法应用于影响随机系统中扩散常数或温度的扰动。在此，我们表明可以使用一个独立的“有效”物理过程来描述受扰动力学，且该动力学反过来能让我们准确计算对扩散变化的响应。有趣的是，该有效动力学包含一个与系统瞬时概率密度的“分数（score）”成正比的额外漂移项——这一对象近年来也在机器学习领域的去噪扩散模型背景下被广泛研究。利用近期开发的用于学习分数的算法，我们表明可以在无法获得精确分数的系统上开展非平衡响应计算。
英文摘要：
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable -- additional dynamical information is needed. The theory of linear response around nonequilibrium steady states relies on path ensemble averaging, which makes this theory inapplicable to perturbations that affect the diffusion constant or temperature in a stochastic system. Here, we show that a separate, ``effective'' physical process can be used to describe the perturbed dynamics and that this dynamics in turn allows us to accurately calculate the response to a change in the diffusion. Interestingly, the effective dynamics contains an additional drift that is proportional to the ``score'' of the instantaneous probability density of the system -- this object has also been studied extensively in recent years in the context of denoising diffusion models in the machine learning literature. Exploiting recently developed algorithms for learning the score, we show that we can carry out nonequilibrium response calculations on systems for which the exact score cannot be obtained.
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