Curie's Symmetry Principle and Heterogeneous Thermodynamic Systems

I am trying to understand the (possible) couplings between scalar chemical reaction phenomena and vectorial phenomena such as heat conduction and mass diffusion. It is argued in the literature that I have read that the usual assumption of cross coefficients for scalar+vectorial phenomena only applies for isotropic systems. Other readings indicate that this is also only true for isotropic and homogeneous systems (that is, isotropy of the system structure, not just its transport properties). The example of active transport across membranes is typically used to explain how such coupling can occur, but because of the thermodynamic complexity of active transport, this example isn't helping me understand exactly when the cross coefficients for scalar+vectorial coupling can or cannot exist.



Will coupling of chemical reactions and vectorial heat and mass fluxes occur in ANY heterogeneous or anisotropic system? For instance, if a crystal is everywhere chemically heterogeneous will this coupling occur everywhere in the crystal? If there are two homogeneous crystals with differently oriented lattices will this coupling occur at their interface?



I don't understand it.