Finding precise signatures of different brain states is a central, unsolved question in neuroscience. We reformulated the problem to quantify the ‘inside out’ balance of intrinsic and extrinsic brain dynamics in brain states. The difference in brain state can be described as differences in the detailed causal interactions found in the underlying intrinsic brain dynamics. We used a thermodynamics framework to quantify the breaking of the detailed balance captured by the level of asymmetry in temporal processing, i.e. the arrow of time. Specifically, the temporal asymmetry was computed by the time-shifted correlation matrices for the forward and reversed time series, reflecting the level of non-reversibility/non-equilibrium. We found precise, distinguishing signatures in terms of the reversibility and hierarchy of large-scale dynamics in three radically different brain states (awake, deep sleep and anaesthesia) in electrocorticography data from non-human primates. Significantly lower levels of reversibility were found in deep sleep and anaesthesia compared to wakefulness. Non-wakeful states also showed a flatter hierarchy, reflecting the diversity of the reversibility across the brain. Overall, this provides signatures of the breaking of detailed balance in different brain states, perhaps reflecting levels of conscious awareness.

The cognitive functions of human and non-human primates rely on the dynamic interplay of distributed neural assemblies. As such, it seems unlikely that cognition can be supported by macroscopic brain dynamics at the proximity of thermodynamic equilibrium. We confirmed this hypothesis by investigating electrocorticography data from non-human primates undergoing different states of unconsciousness (sleep, and anesthesia with propofol, ketamine, and ketamine plus medetomidine), and funcional magnetic resonance imaginga data from humans, both during deep sleep and under propofol anesthesia. Systematically, all states of reduced consciousness unfolded at higher proximity to equilibrium dynamics than conscious wakefulness, as demonstrated by entropy production and the curl of probability flux in phase space. Our results establish non-equilibrium macroscopic brain dynamics as a robust signature of consciousness, opening the way for the characterization of cognition and awareness using tools from statistical mechanics.

We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We use variational autoencoders (VAEs) to embed temporal correlations between coupled nonlinear oscillators that model brain states in the wakesleep cycle into a two-dimensional manifold. Training a VAE with samples generated using two different parameter combinations results in an embedding that encodes the repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first follow this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two end points of this trajectory; then, we show that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology.

Increasing evidence suggests that responsiveness is associated with critical or near-critical cortical dynamics, which exhibit scale-free cascades of spatio-temporal activity. These cascades, or ‘avalanches’, have been detected at multiple scales, from in vitro and in vivo microcircuits to voltage imaging and brain-wide functional magnetic resonance imaging (fMRI) recordings. Criticality endows the cortex with certain information-processing capacities postulated as necessary for conscious wakefulness, yet it remains unknown how unresponsiveness impacts on the avalanche-like behaviour of large-scale human haemodynamic activity. We observed a scale-free hierarchy of co-activated connected clusters by applying a point-process transformation to fMRI data recorded during wakefulness and non-rapid eye movement (NREM) sleep. Maximum-likelihood estimates revealed a significant effect of sleep stage on the scaling parameters of the cluster size power-law distributions. Post hoc statistical tests showed that differences were maximal between wakefulness and N2 sleep. These results were robust against spatial coarse graining, fitting alternative statistical models and different point-process thresholds, and disappeared upon phase shuffling the fMRI time series. Evoked neural bistabilities preventing arousals during N2 sleep do not suffice to explain these differences, which point towards changes in the intrinsic dynamics of the brain that could be necessary to consolidate a state of deep unresponsiveness.