  Using XMM-Newton spatially resolved X-ray imaging spectroscopy we obtain the
temperature, density, entropy, gas mass, and total mass profiles for two groups
of galaxies out to ~0.3 Rvir (Rvir, the virial radius). Our density profiles
agree well with those derived previously, and the temperature data are broadly
consistent with previous results but are considerably more precise. Both of
these groups are at the mass scale of 2x10^13 Msolar but have rather different
properties. They have considerably lower gas mass fractions at r<0.3 Rvir than
the rich clusters. NGC2563, one of the least luminous groups for its X-ray
temperature, has a very low gas mass fraction of ~0.004 inside 0.1 Rvir, which
rises with radius. NGC4325, one of the most luminous groups at the same average
temperature, has a higher gas mass fraction of 0.02. The entropy profiles and
the absolute values of the entropy as a function of virial radius also differ,
with NGC4325 having a value of ~100 keV cm-2 and NGC2563 a value of ~300 keV
cm-2 at r~0.1 Rvir. For both groups the profiles rise monotonically with radius
and there is no sign of an entropy "floor". These results are inconsistent with
pre-heating scenarios which have been developed to explain the entropy floor in
groups but are broadly consistent with models of structure formation which
include the effects of heating and/or the cooling of the gas. The total entropy
in these systems provides a strong constraint on all models of galaxy and group
formation, and on the poorly defined feedback process which controls the
transformation of gas into stars and thus the formation of structure in the
universe.
