given by $$\begin{aligned}
  P_\rmn{e} &=& S_\rmn{e}\,n_\rmn{e}^{\gamma} \\ 
  S_\rmn{e} &=& {T_\rmn{e}\over n_\rmn{e}^{\gamma-1}}, \label{equation:entropy_def}\end{aligned}$$ where $P_\rmn{e}$, $S_\rmn{e}$, $n_\rmn{e}$ and $T_\rmn{e}$ are the electron pressure, entropy, density and temperature (in keV units) respectively. The parameter $\gamma$ is the adiabatic ratio of heat capacities and for an ideal monatomic gas is equal to 5/3. The observable quantity $S_\rmn{e}$ is related to the true thermodynamic entropy per gas particle $S_\rmn{th}$ by the following equation $$S_\rmn{th} = A\ln(S_\rmn{e}) + B,$$ where $A$ and $B$ are both functions of the fundamental and ideal gas constants. At small radii [$r \la 0.1r_{200}$, @Voit:2005] the entropy profiles of clusters are expected to have a low-entropy core region as a result of radiative cooling of the gas. However excess entropy may also exist in this region due to additional heating processes from central AGN and star formation. At the opposite end of the radial scale the accretion of matter at the interface between the cluster gas and the external medium generates an expanding shock-front, with an ever-increasing virial mass and hence infall-velocity. It is therefore expected that the entropy profile increases as a function of radius towards the edge of the cluster. Simulations of non-radiative clusters predict that the entropy 