  The distribution of baryons provides a significant way to understand the
formation of galaxy clusters by revealing the details of its internal structure
and changes over time. In this paper, we present theoretical studies on the
scaled profiles of physical properties associated with the baryonic components,
including gas density, temperature, metallicity, pressure and entropy as well
as stellar mass, metallicity and satellite galaxy number density in galaxy
clusters from $z=4$ to $z=0$ by tracking their progenitors. These mass-complete
simulated galaxy clusters are coming from THE THREE HUNDRED with two runs:
GIZMO-SIMBA and Gadget-X. Through comparisons between the two simulations, and
with observed profiles which are generally available at low redshift, we find
that (1) the agreements between the two runs and observations are mostly at
outer radii $r \gtrsim 0.3r_{500}$, in line with the self-similarity
assumption. While Gadget-X shows better agreements with the observed gas
profiles in the central regions compared to GIZMO-SIMBA; (2) the evolution
trends are generally consistent between the two simulations with slightly
better consistency at outer radii. In detail, the gas density profile shows
less discrepancy than the temperature and entropy profiles at high redshift.
The differences in the cluster centre and gas properties imply different
behaviours of the AGN models between Gadget-X and GIZMO-SIMBA, with the latter,
maybe too strong for this cluster simulation. The high-redshift difference may
be caused by the star formation and feedback models or hydrodynamics treatment,
which requires observation constraints and understanding.
