  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.
