Ginzburg-Landau theory for mass transport in a driven diffusive system

A time-dependent Ginzburg-Landau theory is developed in order to characterize the results of a recent computer simulation on a lattice gas driven by an applied chemical potential gradient acting on the boundaries of the system. In accordance with the simulation results, the system shows a linear density profile above the critical temperature and phase separation below the critical temperature. It is furthermore shown that the driven system is equivalent to an equilibrium system in an applied linearly dependent chemical potential proportional to the current.