Description of data files: Most data files will consist of either 1 column (Entropy) or 3 (Entropy, Mutual Information, Tri-Partite Mutual Information) when applicable (i.e. when the system length is a multiple of 4, corresponding to the variable pc = 4, which describes the partition size under the scheme given in the insets of Figs 3c and 4c). Data was collected over a long time period, therefore conventions differed between data sets. Comparison of filename variables with variables in paper: ----- FIG 2 -----: L: Length of system xr: $\xi_{r}$ str: $\lambda$ dt: $\delta t$ T: The total time for which the simulation runs eT: The time between entropy measurements (we use p in place of decimal points) There is also a realisation number at the end of the file name. ----- Fig 3 and Fig 5 -----: For this dataset there were 100 samples taken at spacings of eT = 1 before T, e.g. if T = 400, then there are 100 samples from t = 300 to 400. For this set, dt = 0.01 unless stated otherwise. L: Length of system pc: The partition size for mutual information measurements P: The probability for measurement to take place (always set to 1) St: $\lambda$ Xs: $\xi_{s}$ Xt: (redundant variable, uniform disorder that varies over time, not applicable to this paper) Xr: $\xi_{r}$ T: The total time for which the simulation runs There is also a realisation number at the end of the file name. Exception for L10 files: xS: $\xi_{s}$ xT: redundant xR: $\xi_{r}$ ----- Fig 4 and Fig 6 -----: Identical convention to Fig 3 and Fig 5.