  Forthcoming large galaxy cluster surveys will yield tight constraints on
cosmological models. It has been shown that in an idealized survey, containing
> 10,000 clusters, statistical errors on dark energy and other cosmological
parameters will be at the percent level. It has also been shown that through
"self-calibration", parameters describing the mass-observable relation and
cosmology can be simultaneously determined, though at a loss in accuracy by
about an order of magnitude. Here we examine the utility of an alternative
approach of self-calibration, in which a parametrized ab-initio physical model
is used to compute cluster structure and the resulting mass-observable
relations. As an example, we use a modified-entropy ("pre-heating") model of
the intracluster medium, with the history and magnitude of entropy injection as
unknown input parameters. Using a Fisher matrix approach, we evaluate the
expected simultaneous statistical errors on cosmological and cluster model
parameters. We study two types of surveys, in which a comparable number of
clusters are identified either through their X-ray emission or through their
integrated Sunyaev-Zel'dovich (SZ) effect. We find that compared to a
phenomenological parametrization of the mass-observable relation, using our
physical model yields significantly tighter constraints in both surveys, and
offers substantially improved synergy when the two surveys are combined. These
results suggest that parametrized physical models of cluster structure will be
useful when extracting cosmological constraints from SZ and X-ray cluster
surveys. (abridged)
