Hot intergalactic gas in clusters, groups, and filaments emanates a continuous background of 0.5-2.0 keV X-rays that ought to be detectable with the new generation of X-ray observatories. Here we present selected results from a program to simulate the surface brightness distribution of this background with an adaptive mesh cosmological hydrodynamics code. We show that the bright end of this distribution is well approximated by combining the cluster temperature function with a beta -model for surface brightness and appropriate luminosity-temperature and core radius-luminosity relations. Our simulations verify that the X-ray background from hot gas vastly exceeds observational limits if nongravitational processes do not modify the intergalactic entropy distribution. An entropy floor similar to 100 keV cm(2), which could be established by either heating or cooling, appears necessary to reconcile the simulated background with observations. Because the X-ray background distribution is so sensitive to the effects of nongravitational processes, it offers a way to constrain the thermal history of the intergalactic medium that is independent of the uncertainties associated with surveys of clusters and groups.
