  Using cosmological simulations of galaxy cluster regions from The Three
Hundred project we study the nature of gas in filaments feeding massive
clusters. By stacking the diffuse material of filaments throughout the cluster
sample, we measure average gas properties such as density, temperature,
pressure, entropy and Mach number and construct one-dimensional profiles for a
sample of larger, radially-oriented filaments to determine their characteristic
features as cosmological objects. Despite the similarity in velocity space
between the gas and dark matter accretion patterns onto filaments and their
central clusters, we confirm some differences, especially concerning the more
ordered radial velocity dispersion of dark matter around the cluster and the
larger accretion velocity of gas relative to dark matter in filaments. We also
study the distribution of shocked gas around filaments and galaxy clusters,
showing that the surrounding shocks allow an efficient internal transport of
material, suggesting a laminar infall. The stacked temperature profile of
filaments is typically colder towards the spine, in line with the cosmological
rarefaction of matter. Therefore, filaments are able to isolate their inner
regions, maintaining lower gas temperatures and entropy. Finally, we study the
evolution of the gas density-temperature phase diagram of our stacked filament,
showing that filamentary gas does not behave fully adiabatically through time
but it is subject to shocks during its evolution, establishing a characteristic
z = 0, entropy-enhanced distribution at intermediate distances from the spine
of about 1 - 2 $h^{-1}$ Mpc for a typical galaxy cluster in our sample.
