Understanding how complex networks respond to perturbations is key to uncovering their functional organization. We show that, for a maximum-entropy perturbation prior, standard diffusion cannot increase response entropy, a measure of the diversity of the system’s response. To overcome this limitation, we develop a density-matrix-based information thermodynamics of perturbation responses along arbitrary dynamical trajectories. We show that this framework is grounded in an information-theoretic principle of least dissipation and introduces a generalized free energy that quantifies deviations from an instantaneous diffusive reference. We then illustrate the formalism using nonlinear complex networks, revealing regimes of enhanced response diversity that cannot be captured by standard diffusive descriptions.