= Solution
Away from singular regimes, assume <enthalpy> and <heat capacity at constant pressure> are extensive: $\langle H\rangle=Nh$ and $C_P=Nc_P$, with nonzero intensive $h$. The <enthalpy fluctuation formula> then gives
$$
\boxed{\frac{\sqrt{\operatorname{Var}(H)}}{|\langle H\rangle|}
=\frac{\sqrt{k_BT^2c_P}}{|h|\sqrt N}}.
$$
Absolute fluctuations grow as $\sqrt N$, while the <mean> grows as $N$. In the <thermodynamic limit>, <enthalpy> per particle therefore concentrates around its <mean>; it is relative, rather than absolute, fluctuations that vanish. This is the usual <relative fluctuations of an extensive observable> scaling. It assumes ordinary extensive <heat capacity> and a nonzero <mean> with a stated <energy> reference; a critical divergence or an artificially zero <mean> requires separate analysis.
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