Galaxy groups differ from clusters primarily by way of their lower masses , M \sim 10 ^ { 14 } M _ { \odot } vs . M \sim 10 ^ { 15 } M _ { \odot } .
We discuss how mass affects the thermal state of the intracluster or the intragroup medium , specifically as to their entropy levels and radial profiles .
We show that entropy is produced in both cases by the continuing inflow of intergalactic gas across the system boundary into the gravitational potential well .
The inflow is highly supersonic in clusters , but weakly so in groups .
The former condition implies strong accretion shocks with substantial conversion of a large inflow kinetic into thermal energy , whereas the latter condition implies less effective conversion of lower energies .
These features produce a conspicuous difference in entropy deposition at the current boundary .
Thereafter , adiabatic compression of the hot gas into the potential well converts such time histories into radial profiles throughout a cluster or a group .
In addition , in both cases a location of the system at low z in the accelerating universe or in a poor environment will starve out the inflow and the entropy production , and produce flattening or even bending down of the outer profile .
We analyze in detail the sharp evidence provided by the two groups ESO 3060170 and RXJ1159+5531 that have been recently observed in X rays out to their virial radii , and find a close and detailed match with our expectations .