The influence of flux balance on the generalized chemical potential in mass transport models

In equilibrium systems, the conservation of the number of particles (or mass) leads to the equalization of the chemical potential throughout the system. Using a non-equilibrium generalization of the notion of a chemical potential, we investigate the influence of the balance of mass fluxes on the generalized chemical potential in the framework of stochastic mass transport models. We focus specifically on the issue of local measurements of the chemical potential. We find that the presence of a branching geometry leads to unequal local measurement results at different points of the system. We interpret these results in terms of mass flux balance, and argue that the conditions for the global definition of the chemical potential still hold, but that local measurements fail to capture the global theoretical value.