  We present infrared luminosity functions and dust mass functions for the
EAGLE cosmological simulation, based on synthetic multi-wavelength observations
generated with the SKIRT radiative transfer code. In the local Universe, we
reproduce the observed infrared luminosity and dust mass functions very well.
Some minor discrepancies are encountered, mainly in the high luminosity regime,
where the EAGLE-SKIRT luminosity functions mildly but systematically
underestimate the observed ones. The agreement between the EAGLE-SKIRT infrared
luminosity functions and the observed ones gradually worsens with increasing
lookback time. Fitting modified Schechter functions to the EAGLE-SKIRT
luminosity and dust mass functions at different redshifts up to $z=1$, we find
that the evolution is compatible with pure luminosity/mass evolution. The
evolution is relatively mild: within this redshift range, we find an evolution
of $L_{\star,250}\propto(1+z)^{1.68}$,
$L_{\star,\text{TIR}}\propto(1+z)^{2.51}$ and
$M_{\star,\text{dust}}\propto(1+z)^{0.83}$ for the characteristic
luminosity/mass. For the luminosity/mass density we find
$\varepsilon_{250}\propto(1+z)^{1.62}$,
$\varepsilon_{\text{TIR}}\propto(1+z)^{2.35}$ and
$\rho_{\text{dust}}\propto(1+z)^{0.80}$, respectively. The mild evolution of
the dust mass density is in relatively good agreement with observations, but
the slow evolution of the infrared luminosity underestimates the observed
luminosity evolution significantly. We argue that these differences can be
attributed to increasing limitations in the radiative transfer treatment due to
increasingly poorer resolution, combined with a slower than observed evolution
of the SFR density in the EAGLE simulation and the lack of AGN emission in our
EAGLE-SKIRT post-processing recipe.
