  The recent reported discovery of a low-mass $z=5.2$ and an intermediate-mass
$z=7.3$ quenched galaxy with JWST/NIRSpec is the first evidence of halted star
formation above $z\approx 5$. Here we show how bursty star formation at $z=4-8$
gives rise to temporarily quenched, or mini-quenched galaxies in the mass range
$M_{\star} = 10^7-10^9 \ M_{\odot}$ using four models of galaxy formation: the
periodic box simulation IllustrisTNG, the zoom-in simulations VELA and
FirstLight and an empirical halo model. The main causes for mini-quenching are
stellar feedback, lack of gas accretion onto galaxies and galaxy-galaxy
interactions. The abundance of (mini-)quenched galaxies agrees across the
models: the population first appears below $z\approx 8$, after which their
proportion increases with cosmic time, from $\sim 0.5-1.0$% at $z=7$ to $\sim
2-4$% at $z=4$, corresponding to comoving number densities of $\sim 10^{-5}$
Mpc$^{-3}$ and $\sim 10^{-3}$ Mpc$^{-3}$, respectively. These numbers are
consistent with star formation rate duty cycles inferred for VELA and
FirstLight galaxies. Their star formation histories (SFHs) suggest that
mini-quenching at $z=4-8$ is short-lived with a duration of $\sim 20-40$ Myr,
which is close to the free-fall timescale of the inner halo. However, mock
spectral energy distributions of mini-quenched galaxies in IllustrisTNG and
VELA do not match JADES-GS-z7-01-QU photometry, unless their SFHs are
artificially altered to be more bursty on timescales of $\sim 40$ Myr. Studying
mini-quenched galaxies might aid in calibrating sub-grid models governing
galaxy formation, as these may not generate sufficient burstiness at high
redshift to explain the SFH inferred for JADES-GS-z7-01-QU.
