(Abridged) The thermal state of the intracluster medium results from a competition between gas cooling and heating. The heating comes from two distinct sources: gravitational heating from the collapse of the dark matter halo and thermal input from galaxy/black hole formation. However, a long standing problem has been that cosmological simulations based on smoothed particle hydrodynamics (SPH) and Eulerian mesh codes predict different results even when cooling and galaxy/black hole heating are switched off. Clusters formed in SPH simulations show near powerlaw entropy profiles, while those formed in mesh simulations develop a core and do not allow gas to reach such low entropies. Since the cooling rate is closely connected to the minimum entropy of the gas, the differences are of potentially key importance. In this paper, we investigate the origin of this discrepancy. By comparing simulations run using the GADGET-2 SPH code and the FLASH adaptive Eulerian mesh code, we show that the discrepancy arises during the idealised merger of two clusters. The difference is not sensitive to the resolution of our simulations, nor is it is due differences in the gravity solvers, Galilean non-invariance of the mesh code, or an effect of unsuitable artificial viscosity in the SPH code. Instead, we find that the difference is inherent to the treatment of eddies and fluid instabilities. These are suppressed in the SPH simulations, while the cluster mergers generate strong vortices in the mesh simulations that efficiently mix the fluid and erase the low entropy gas. Consequently, particles in the SPH simulations retain a close connection to their initial entropy, while this connection is much weaker in the mesh simulations. We discuss the potentially profound implications of these results.
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