= Model A fluctuation-dissipation relation
For <nonconserved order-parameter dynamics>, <microscopic reversibility> with equilibrium weight proportional to $e^{-F/(k_BT)}$ requires
$$
\sigma^2=2\Gamma k_BT.
$$
Indeed the <Onsager--Machlup path probability> gives $\log(P_F/P_B)=-2\Gamma\int\dot p\,\delta F/\delta p\,dt/\sigma^2=-2\Gamma(F_2-F_1)/\sigma^2$. Equating this to the <detailed balance> value proves the relation. The <functional chain rule> is understood with the same midpoint convention as the path action.
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