Many networked dynamical systems are embedded in larger environments whose degrees of freedom are too numerous, inaccessible, or simply unnecessary to track explicitly.  Yet eliminating these degrees of freedom can fundamentally change the effective dynamics of the subsystem of interest, introducing memory, structured forcing, and nontrivial pathways of influence.  This talk develops a mathematical framework for understanding these effects in linear agent-based systems, using opinion dynamics as a concrete setting.   By partitioning a network into an observed system and an unobserved environment, we show how exact elimination of the environmental variables yields a generalized Langevin equation (GLE).  The resulting memory kernel and environmental forcing are determined explicitly by the block structure of the underlying dynamical operator.  This representation connects network topology to relaxation timescales, reveals how influence propagates across system–environment boundaries, and provides a basis for defining dynamical measures of influence and vulnerability that depend on both the direction and timescale of propagation.  It also identifies environmental agents whose intervention can most effectively control the observed population.   The same framework provides a route to deriving, rather than postulating, stochastic properties of collective dynamics.  When uncertainty in the initial environmental state is modeled statistically, the reduced forcing has an explicitly computable covariance.  Under precise structural conditions, this covariance satisfies a fluctuation–dissipation relation with the memory kernel, yielding an emergent social temperature that can be related to measurable opinion variance.  Directed interactions and heterogeneous agent susceptibilities expose the limits of this scalar description and lead to more general, network-dependent fluctuation structures.   Together, these results illustrate how exact reduction, operator theory, and network structure can unify the analysis of memory, influence, control, and fluctuations in open dynamical systems, with potential applications extending beyond social networks to other linear models of interacting populations.