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Context. There has been significant technological and scientific progress in our ability to detect, monitor, and model the physics of γ -ray bursts (GRBs) over the 50 years since their first discovery. However, the dissipation process thought to be responsible for their defining prompt emission is still unknown. Recent efforts have focused on investigating how the ultrarelativistic jet of the GRB propagates through the progenitor’s stellar envelope for different initial composition shapes, jet structures, magnetisation, and, consequently, possible energy dissipation processes. Study of the temporal variability – in particular the shortest duration of an independent emission episode within a GRB – may provide a unique way to distinguish the imprint of the inner engine activity from geometry and propagation related effects. The advent of new high-energy detectors with exquisite time resolution now makes this possible. Aims. We aim to characterise the minimum variability timescale (MVT) defined as the shortest duration of individual pulses that shape a light curve for a sample of GRBs in the keV–MeV energy range and test correlations with other key observables such as the peak luminosity, the Lorentz factor, and the jet opening angle. We compare these correlations with predictions from recent numerical simulations for amore »relativistic structured – possibly wobbling – jet and assess the value of temporal variability studies as probes of prompt-emission dissipation physics. Methods. We used the peak detection algorithm MEPSA to identify the shortest pulse within a GRB time history and preliminarily calibrated MEPSA to estimate the full width at half maximum duration. We then applied this framework to two sets of GRBs: Swift GRBs (from 2005 to July 2022) and Insight Hard Modulation X-ray Telescope (Insight-HXMT) GRBs (from June 2017 to July 2021, including the exceptional 221009A). We then selected 401 GRBs with measured redshift to test for correlations. Results. We confirm that, on average, short GRBs have significantly shorter MVTs than long GRBs. The MVT distribution of short GRBs with extended emission such as 060614 and 211211A is compatible only with that of short GRBs. This is important because it provides a new clue concerning the progenitor’s nature. The MVT for long GRBs with measured redshift anti-correlates with peak luminosity; our analysis includes careful evaluation of selection effects. We confirm the anti-correlation with the Lorentz factor and find a correlation with the jet opening angle as estimated from the afterglow light curve, along with an inverse correlation with the number of pulses. Conclusions. The MVT can identify the emerging putative new class of long GRBs that are suggested to be produced by compact binary mergers. For otherwise typical long GRBs, the different correlations between MVT and peak luminosity, Lorentz factor, jet opening angle, and number of pulses can be explained within the context of structured, possibly wobbling, weakly magnetised relativistic jets.« less