  The dissipation process of GRB prompt emission is still unknown. Study of
temporal variability may provide a unique way to discriminate the imprint of
the inner engine activity from geometry and propagation related effects. We
define the minimum variability timescale (MVT) as the shortest duration of
individual pulses that shape a light curve for a sample of GRBs and test
correlations with peak luminosity, Lorentz factor, and jet opening angle. We
compare these correlations with predictions from recent numerical simulations
for a relativistic structured -- possibly wobbling -- jet and assess the value
of MTV as probe of prompt-emission physics. We used the peak detection
algorithm mepsa to identify the shortest pulse within a GRB time history and
estimate its full width half maximum (FWHM). We applied this framework to two
sets of GRBs: Swift (from 2005 to July 2022) and Insight-HXMT (from June 2017
to July 2021, including 221009A). We then selected 401 GRBs with measured z to
test for correlations. On average short GRBs have significantly shorter MVT
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 provides
a new clue on the progenitor's nature. The MVT for long GRBs anticorrelates
with peak luminosity. We confirm the anticorrelation with the Lorentz factor
and find a correlation with the jet opening angle as estimated from the
afterglow, along with an inverse correlation with the number of pulses. 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.
(summarised)

High Energy Astrophysical Phenomena