[punk_cat]

I have the following system of reactions

[tex] \ce{X_1 + Y_1 <=>[k21][k12] X_2}, \ce{X_2 <=>[k32][k23] X_3}, \ce{X_3 <=>[k13][k31] X_1 + Y_2},[/tex]
 [tex] \ce{X_2 + Y_3 <=>[k42][k24] X_4},  \ce{X_4 <=>[k34][k43] X_3 + Y_4}.[/tex]


Here  {X_I| ∈ {1, . . . , 4}} represents the state of the molecule that catalyzes the reaction and {Y_I | ∈ {1, . . . , 4}} represents a reactant or product that is consumed or produced by the reaction.

I need to find the free energy flow J_G with respect to Y and the entropy generation R_S with respect to X.

Could anyone recommend the approach to this problem?