  The brain is a non-equilibrium system whose dynamics change in different
brain states, such as wakefulness and deep sleep. Thermodynamics provides the
tools for revealing these non-equilibrium dynamics. We used violations of the
fluctuation-dissipation theorem to describe the hierarchy of non-equilibrium
dynamics associated with different brain states. Together with a whole-brain
model fitted to empirical human neuroimaging data, and deriving the appropriate
analytical expressions, we were able to capture the deviation from equilibrium
in different brain states that arises from asymmetric interactions and
hierarchical organisation.
