E${}^2$Sim: Long-Horizon Simulation of Everyday Human Behavior with Evolving States

AI agents are increasingly expected to support users over long periods, across projects, work, and daily life. This requires modeling not only who users are, but also how their goals, interests, activities, and interactions evolve over time. A central challenge in longitudinal user simulation is maintaining consistency between these evolving states and the consequences of actions in a shared environment. We introduce E${}^2$Sim, a longitudinal user simulation framework that jointly models evolving actor states and a dynamic shared environment. E${}^2$Sim connects actor-state updates with shared-world changes through a feedback loop linking immediate actions, delayed outcomes, and actor-specific observations across work and life. This allows the consequences of earlier actions to shape later behavior across work and life, while preserving differences in what each actor knows. We further propose a suite of longitudinal trajectory diagnostics tailored to longitudinal simulation, measuring dynamic consistency, coherent event progression and collaboration, and non-degenerate trajectory development rather than static consistency alone. In one 60-day simulation, E${}^2$Sim produced more extracted event threads judged meaningful by our evaluator and fewer near-duplicate actions than four direct-generation baselines. Together, the framework and evaluation methods provide a basis for studying longitudinal user simulation, with potential applications in training and evaluating AI agents that assist users over extended periods.