Model
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We test the ability of the entropy-based model described in Section\[section:entropy\_model\] to reproduce the known properties of galaxy clusters by fitting to simulated SZ and X-ray surface brightness data. We simulate SZ data from the CBI2 31GHz interferometer and typical X-ray surface brightness data from the EPIC camera on *XMM-Newton*.

Mock CBI2 SZ data {#section:mock_sz_data}
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The sky signal for the simulated CBI2 observation is generated from summing the SZ and intrinsic CMB components. The SZ thermodynamic temperature for a simulated galaxy cluster is calculated from the electron pressure using Equation\[equation:sz\_temp\]. The CMB temperature map is constructed from an angular power spectrum generated using CMBFAST [^2] [@Seljak:1996], assuming a flat $\Lambda$CDM cosmology with $\Omega_\rmn{M} = 0.3$, $\Omega_{\Lambda} = 0.7$ and $h = 0.7$. The SZ and CMB thermodynamic temperature maps are converted to sky brightness units for each of the 10 frequency channels (26-36GHz) using the differential form of the Planck equation $${\rmn{d}I_{\nu}\over \rmn{d}T} =
  {2k_\rmn{B}\nu^{2}\over c^{2}}x^{2}\rmn{e}^{x}(\rmn{e}^{x} -
  1)^{-2},$$ where $T$ is the thermodynamic temperature and $x =
h\nu/k_\rmn{B}T_\rmn{CMB}$. The two brightness maps are then summed to form a combined sky simulation.

The sky brightness map is multiplied by the CBI2 primary beam and fast Fourier transformed to 