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arXiv · 2601.16387

Fluctuation-Response Theory for Nonequilibrium Langevin Dynamics

Hyun-Myung Chun·Euijoon Kwon·Hyunggyu Park·Jae Sung Lee
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Abstract

We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that generalizes the fluctuation-dissipation theorem from equilibrium to nonequilibrium settings. This relation connects global fluctuations of observables with their local responses to perturbations in force, mobility, and temperature. We further derive finite-time fluctuation-response inequalities, leading to response uncertainty relations that complement the identity by providing more practical bounds. These derivations establish a unified theoretical framework linking the fluctuation-dissipation theorem and thermodynamic uncertainty relations. Using the $F_1$-ATPase molecular motor model, we illustrate how these response-based bounds constrain the long-time diffusion coefficient.

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Hyun-Myung Chun, Euijoon Kwon, Hyunggyu Park, Jae Sung Lee. 2026-01-23. Fluctuation-Response Theory for Nonequilibrium Langevin Dynamics. https://arxiv.org/abs/2601.16387

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