  We use the cosmo-OWLS suite of cosmological hydrodynamical simulations to
investigate the scatter and evolution of the global hot gas properties of large
simulated populations of galaxy groups and clusters. Our aim is to compare the
predictions of different physical models and to explore the extent to which
commonly-adopted assumptions in observational analyses (e.g. self-similar
evolution) are violated. We examine the relations between (true) halo mass and
the X-ray temperature, X-ray luminosity, gas mass, Sunyaev-Zel'dovich (SZ)
flux, the X-ray analogue of the SZ flux ($Y_X$) and the hydrostatic mass. For
the most realistic models, which include AGN feedback, the slopes of the
various mass-observable relations deviate substantially from the self-similar
ones, particularly at late times and for low-mass clusters. The amplitude of
the mass-temperature relation shows negative evolution with respect to the
self-similar prediction (i.e. slower than the prediction) for all models,
driven by an increase in non-thermal pressure support at higher redshifts. The
AGN models predict strong positive evolution of the gas mass fractions at low
halo masses. The SZ flux and $Y_X$ show positive evolution with respect to
self-similarity at low mass but negative evolution at high mass. The scatter
about the relations is well approximated by log-normal distributions, with
widths that depend mildly on halo mass. The scatter decreases significantly
with increasing redshift. The exception is the hydrostatic mass-halo mass
relation, for which the scatter increases with redshift. Finally, we discuss
the relative merits of various hot gas-based mass proxies.
