Agent-based models typically treat systems in isolation, discarding environmental coupling as either computationally prohibitive or dynamically irrelevant. We demonstrate that this neglect misses essential physics: environmental degrees of freedom create memory effects that fundamentally alter system dynamics. By systematically transforming linear update rules into exact generalized Langevin equations, we show that unobserved environmental agents manifest as memory kernels whose timescales and coupling strengths are determined by the environmental interaction spectrum. Network topology shapes this memory structure in distinct ways: small-world rewiring drives dynamics toward a single dominant relaxation mode, while fragmented environments sustain multiple persistent modes corresponding to isolated subpopulations. We apply this framework to covert influence operations where adversaries manipulate target populations exclusively via environmental intermediaries. The steady-state response admits a random-walk interpretation through hitting probabilities, revealing how zealot opinions diffuse through the environment to shift system agent opinions toward the zealot mean - even when zealots never directly contact targets.

翻译：基于代理的模型通常将系统视为孤立系统，将环境耦合视为计算上不可行或动态上无关紧要的因素而予以忽略。我们证明这种忽略遗漏了本质物理：环境自由度会产生记忆效应，从根本上改变系统动力学。通过将线性更新规则系统性地转化为精确的广义朗之万方程，我们证明未观测的环境代理表现为记忆核，其时间尺度和耦合强度由环境相互作用谱决定。网络拓扑以不同方式塑造这种记忆结构：小世界重连驱动动力学趋向单一主导弛豫模式，而碎片化环境则维持对应于孤立亚群体的多个持续模式。我们将此框架应用于隐蔽影响行动，其中对手仅通过环境中介操纵目标群体。稳态响应可通过击中概率进行随机游走解释，揭示了狂热者观点如何通过环境扩散，使系统代理观点向狂热者均值偏移——即使狂热者从未直接接触目标。