I have the following system of reactions:
$$ \begin{aligned} \ce{X_1 + Y_1 &<=>[$k_{21}$][$k_{12}$] X_2} \\ \ce{X_2 &<=>[$k_{32}$][$k_{23}$] X_3} \\ \ce{X_3 &<=>[$k_{13}$][$k_{31}$] X_1 + Y_2} \\ \ce{X_2 + Y_3 &<=>[$k_{42}$][$k_{24}$] X_4} \\ \ce{X_4 &<=>[$k_{34}$][$k_{43}$] X_3 + Y_4} \end{aligned} $$
Here $\ce{X_1},\ldots,\ce{X_4}$ represent the state of the molecule that catalyzes the reaction, and $\ce{Y_1},\dots,\ce{Y_4}$ represent a reactant or a product that is consumed or produced by the reaction.
I need to find the free energy flow $J_G$ with respect to $\ce{Y}$ and the entropy generation $R_S$ with respect to $\ce{X}.$
Could anyone recommend the approach to this problem?