The quest for reliable and objective measures of consciousness is critical in basic and clinical neuroscience. Across species, the perturbational complexity index (PCI) has emerged as a robust empirical marker by directly perturbing the brain, yet its relationship to broader physical principles remains unclear. Here, we address this gap by introducing a non-invasive framework based on generative whole-brain models of non-equilibrium brain dynamics. Using these models, we identify violations of the fluctuation-dissipation theorem (FDT) in humans and rodents across wakefulness, anesthesia, and disorders of consciousness (DoC). Mirroring PCI, FDT violations decrease in unresponsive DoC and anesthesia compared with conscious conditions. These findings reveal a robust empirical link between PCI and non-equilibrium dynamics in spontaneous brain signals, suggesting that non-equilibrium dynamics capture an important aspect of perturbational complexity. Overall, this framework opens non-invasive, model-based avenues for understanding consciousness and supports efforts to assess its loss and recovery in health and disease.