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The first passage is a generic concept for quantifying when a random quantitysuch as the position of a diffusing molecule or the value of a stock crosses apreset threshold (target) for the first time. The last decade saw anenlightening series of new results focusing mostly on the so-called mean andglobal first passage time (MFPT and GFPT, respectively) of such processes. Herewe push the understanding of first passage processes a step further. For asimple heterogeneous system we derive rigorously the complete distribution offirst passage times (FPTs). Our results demonstrate that the typical FPTsignificantly differs from the MFPT, which corresponds to the long timebehaviour of the FPT distribution. Conversely, the short time behaviour isshown to correspond to trajectories connecting directly from the initial valueto the target. Remarkably, we reveal a previously overlooked thirdcharacteristic time scale of the first passage dynamics mirroring briefexcursion away from the target.

First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time