We use a simple model to extend network models for activated dynamics to a continuous landscape with a well-defined notion of distance and a direct connection to many-body systems. The model consists of a tracer in a high-dimensional funnel landscape with no disorder. We find a nonequilibrium low-temperature phase with aging dynamics that is effectively equivalent to that of models with built-in disorder, such as the trap model, step model and random energy model. Finally, we compare entropy with energy-driven activation, and we remark that the former is more robust to the choice of the dynamics since it does not depend on whether one uses local or global updates.