Fig 2.

(a) The system traces out the minimum contour on the energy surface, indicated by the heat map, where red indicates high energy and blue indicates low energy. The energy surface is a function of anaesthetic concentration and the state of the system as conscious or unconscious computed according to Equation (1). The red arrows indicate the trajectory the system will take as anaesthetic concentration is raised from zero, and the blue arrows indicate the trajectory when lowered from maximal. Note that the induction arm stays in the ‘awake’ minimum until the local minimum disappears, when the trajectory abruptly shifts to the ‘anaesthetised’ minimum. The converse happens when the system starts anaesthetised and the concentration decreases, producing hysteresis. (b) Once additive noise is included in the system, hysteresis collapses over time. For an intermediate anaesthetic concentration ($E{C}_{50}$ in this case), we simulate the behaviour of the system that starts out in the awake state for a progressively larger number of time steps. The number of steps is shown above each panel (100 simulations were used). The distribution of data eventually converges to the expected even split between the awake and. (c) The magnitude of the noise can affect perception of system state. Both traces represent the results of a simulation for a single brain flickering between the awake and anaesthetised states. In the upper trace, the noise term is much smaller than the lower trace, giving the impression that the upper trace is more ‘awake’. Yet the two systems have the same probability of being in the anaesthetised and awake states.