We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein-Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation-dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one, two, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation.

中文翻译：

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有源物质系统中的波动-耗散关系

我们通过研究主动 Ornstein-Uhlenbeck 粒子 (AOUP) 模型的线性响应来研究自推进粒子的非平衡特性。我们根据在没有扰动的情况下计算的相关性来表达线性响应，提出了一个特别紧凑和可读的波动耗散关系 (FDR)：这样的表达式明确地将平衡和非平衡贡献归因于自推进。作为案例研究，我们考虑限制在单井和双井势中的非相互作用 AOUP。在前一种情况下，我们还揭示了维度的影响，研究了一维、二维和三维动力学。我们表明可以从 FDR 推导出关于与平衡距离的信息，