Comparison of the main thermochemical properties of the standard simulation with observations of the local diffuse ISM. Top: comparison of the observational dataset of the HI-to-H₂ transition of Paper I (black points) to the 2D probability histogram obtained with the standard simulation after application of the reconstruction algorithm (see Sect. 3.8 of Paper I). Observations include detections of H₂ (circles) and upper limits on its column density (arrows). The color-coding indicates the fraction of lines of sight (in logarithmic scale) contained in each bin. Bottom: probability distribution function of the thermal pressure of the cold neutral medium in the standard simulation (blue histograms) compared with the probability distribution function of the thermal pressure deduced from the observation of the fine structure levels of carbon (Jenkins & Tripp 2011; black curve). Both distributions are normalized to their maximum value to facilitate comparison.