  Much of the theory on chemical-reaction networks (CRNs) has been developed in
the ideal-solution limit, where interactions between the solutes are
negligible. However, there is a large variety of phenomena in biological cells
and soft-matter physics which appear to deviate from the ideal-solution
behaviour. Particularly striking is the case of liquid-liquid phase separation,
which is typically caused by inter-particle interactions. Here, we revisit a
number of known results in the domain of ideal CRNs, and we generalise and
adapt them to arbitrary interactions between the solutes which stem from a
given free energy. Among these is the form of the steady-state probability
distribution and Lyapunov functions for complex-balanced networks, where the
creation and annihilation rates are equal for all chemical complexes which
appear as reactants or products in the CRN. Finally, we draw a phase diagram
for complex-balanced reaction-diffusion solutions based on the minimisation of
such Lyapunov function with a rationale similar to that of equilibrium
thermodynamics, but for systems that may sustain non-equilibrium chemical
currents at steady state. Nevertheless, we find that complex-balanced networks
are not sufficient to create diffusion currents at steady state.
