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-Zeldovich (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.
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