Polar molecular field (source code)

= Polar molecular field
{title2=$h_i=\delta F/\delta p_i$}

The polar molecular field is the <functional derivative> of the <free energy> with respect to the <polar order parameter>. In the positive-derivative convention, dissipative dynamics is $D_t\mathbf p=-\Gamma\mathbf h$ with positive <kinetic coefficient>. For a quartic local term and an isotropic gradient penalty,
$$
h_i=(a+b|\mathbf p|^2)p_i-\kappa\nabla^2p_i.
$$
Some authors instead define the molecular field with a minus sign, which changes the associated stress and evolution conventions.