  We present high-resolution cosmological hydrodynamic simulations of three
galaxy clusters employing a two-temperature model for the intracluster medium.
We show that electron temperatures in cluster outskirts are significantly lower
than the mean gas temperature, because Coulomb collisions are insufficient to
keep electrons and ions in thermal equilibrium. This deviation is larger in
more massive and less relaxed systems, ranging from 5% in relaxed clusters to
30% for clusters undergoing major mergers. The presence of non-equilibrium
electrons leads to significant suppression of the SZE signal at large
cluster-centric radius. The suppression of the electron pressure also leads to
an underestimate of the hydrostatic mass. Merger-driven, internal shocks may
also generate significant populations of non-equilibrium electrons in the
cluster core, leading to a 5% bias on the integrated SZ mass proxy during
cluster mergers.
