We derive generalized fluctuation–dissipation relations (FDR) holding for a general stochastic dynamics that includes as subcases both equilibrium models for passive colloids and non-equilibrium models used to describe active particles. The relations reported here differ from previous formulations of the FDR because of their simplicity: they require only the microscopic knowledge of the dynamics instead of the whole expression of the steady-state probability distribution function that, except for linear interactions, is unknown for systems displaying non-vanishing currents. From the response function, we can extrapolate generalized versions of the mesoscopic virial equation and the equipartition theorem, which still holds far from equilibrium. Our results are tested in the case of equilibrium colloids described by underdamped or overdamped Langevin equations and for models describing the non-equilibrium behavior of active particles. Both the active Brownian particle and the active Ornstein–Uhlenbeck particle models are compared in the case of a single particle confined in an external potential.

我们推导出广义波动-耗散关系 (FDR)，适用于一般随机动力学，其中包括用于描述活性粒子的被动胶体的平衡模型和非平衡模型作为子情况。这里报告的关系不同于之前的 FDR 公式，因为它们很简单：它们只需要动力学的微观知识，而不是稳态概率分布函数的整个表达式，除了线性相互作用，系统显示未知非零电流。从响应函​​数中，我们可以推断出介观维里方程和均分定理的广义版本，它们仍然远非均衡。我们的结果在由欠阻尼或过阻尼朗之万方程描述的平衡胶体和描述活性粒子非平衡行为的模型的情况下进行了测试。活性布朗粒子和活性 Ornstein-Uhlenbeck 粒子模型在单个粒子被限制在外部电位的情况下进行了比较。