Tackling master equations with a flux loop transform

A procedure is introduced which allows to represent the dynamics of a non-equilibrium system violating detailed balance by its steady state loop fluxes. It is shown that detailed balance is restored in this representation, such that the non-equilibrium steady state follows a simple Boltzmann distribution. A novel algorithm for the construction of the steady state densities naturally emerges, as well as an expression for a 'free energy' functional which attains a minimum in the steady state.