  The temperature and density of the hot diffuse medium pervading galaxy groups
and clusters combine into one significant quantity, the entropy. Here we
express the entropy levels and profiles in model-independent forms by joining
two observables, the X-ray luminosity and the change in the CMB intensity due
to the Sunyaev-Zel'dovich (SZ) effect. Thus we present both global scaling
relations for the entropy levels from clusters and groups, and a simple
expression yielding the entropy profiles in individual clusters from resolved
X-ray surface brightness and SZ spatial distributions. We propose that our
approach provides two useful tools for comparing large data samples with
models, in order to probe the processes that govern the thermal state of the
hot intracluster medium. The feasibility of using such a diagnostic for the
entropy is quantitatively assessed, based on current X-ray and upcoming SZ
measurements.
