The intrinsic dynamics of neuronal circuits shape information processing and cognitive function. Combining non-invasive neuroimaging with anaesthetic-induced suppression of information processing provides a unique opportunity to understand how local dynamics mediate the link between neurobiology and the organism's functional repertoire. To address this question, we compile a unique dataset of multi-scale neural activity during wakefulness and anesthesia encompassing human, macaque, marmoset, mouse and nematode. We then apply massive feature extraction to comprehensively characterize local neural dynamics across > 6 000 time-series features. Using dynamics as a common space for comparison across species, we identify a phylogenetically conserved dynamical profile of anaesthesia that encompasses multiple features, including reductions in intrinsic timescales. This dynamical signature has an evolutionarily conserved spatial layout, covarying with transcriptional profiles of excitatory and inhibitory neurotransmission across human, macaque and mouse cortex. At the network level, anesthetic-induced changes in local dynamics manifest as reductions in inter-regional synchrony. This relationship between local dynamics and global connectivity can be recapitulated using a connectome-based computational model. Finally, this dynamical regime of anaesthesia is experimentally reversed by deep-brain stimulation of the centromedian thalamus in the macaque, resulting in restored arousal and behavioural responsiveness. Altogether, comprehensive dynamical phenotyping reveals that spatiotemporal isolation of local neural activity during anesthesia is conserved across species and anesthetics.