The jump you are seeing is not a sudden change of eg energy or step size, but the difference between the two different chain. Basically, different chains are exploring a different parameter shape, and the mixing is quite poor (hence the few numbers of effective samples and the Gelman-Rubin statistic is higher than 1.4). If you plot the trace plot the chains are likely not overlapping.
PDEs are difficult to fit, cc @aseyboldt and @michaelosthege who have more experience.