= Quenched disorder
{title2=$F_{\rm q}=-k_BT\,\mathbb E_J\log Z_J$}
<Quenched disorder> is randomness held fixed while the other degrees of freedom equilibrate. For a sample with couplings $J$, first compute its <partition function> $Z_J$ and <Helmholtz free energy> $-k_BT\log Z_J$, then average over samples. One must not silently replace $\mathbb E_J\log Z_J$ by $\log\mathbb E_J Z_J$.<Out of equilibrium dynamics of complex systems by Leticia Fernanda Cugliandolo>[§4.2, pp. 83–86, averaging the free energy after computing each fixed-disorder partition function]{ref}
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