Nonequilibrium potentials for local codimension-2 bifurcations of dissipative flows

Nonequilibrium potentials are constructed which serve as macroscopic generalized thermodynamic potentials in dissipative systems far from thermodynamic equilibrium undergoing a local bifurcation of codimension 2 of a fixed point. The cases of two vanishing linear stability coefficients, of one vanishing and one purely imaginary pair, and of two purely imaginary pairs of linear stability coefficients are treated. As a result we establish the existence and form of a nonequilibrium potential for systems sufficiently close to codimension-1 or codimension-2 bifurcations for all cases where locally stable attractors exist in the phase diagram in parameter space. The attractors of the system, their basins of attraction in configuration space, and their bifurcations are determined by extremum properties of the nonequilibrium potentials.