With constant positive <kinetic coefficient> $\Gamma$ and <mobility> $M$, two independent relaxation channels give
$$
\dot p_j=-\partial_iW_{ij}-\Gamma\mu_j+f_j,
\qquad W_{ij}=-M\partial_i\mu_j+N_{ij},
\qquad\mu_j=\frac{\delta F}{\delta p_j}.
$$
The deterministic mobility operator is $\Gamma-M\nabla^2$. Each channel separately satisfies <microscopic reversibility> when its noise obeys the corresponding <Model A fluctuation-dissipation relation> or <fluctuation-dissipation relation for a conserved flux>.


 Mixed conserved and nonconserved order-parameter dynamics

ID: mixed-conserved-and-nonconserved-order-parameter-dynamics