The brain is able to sustain many different states as shown by the daily natural transitions between wakefulness and sleep. Yet, the underlying complex dynamics of these brain states are essentially in nonequilibrium. Here, we develop a thermodynamical formalism based on the off-equilibrium extension of the fluctuation-dissipation theorem (FDT) together with a whole-brain model. This allows us to investigate the nonequilibrium dynamics of different brain states and more specifically to apply this formalism to wakefulness and deep sleep brain states. We show that the off-equilibrium thermodynamical signatures of brain states are significantly different in terms of the overall level of differential and integral violation of FDT. Furthermore, the framework allows for a detailed understanding of how different brain regions and networks are contributing to the off-equilibrium signatures in different brain states. Overall, this framework shows great promise for characterizing and differentiating brain states in health and disease. Published by the American Physical Society 2025