The analytic properties of nonequilibrium potentials are studied in a class of two-variable models undergoing a bifurcation of codimension higher than 1. Several methods for the construction of nonequilibrium potentials are given. Cases are exhibited explicitly where a polynomial expansion does not exist due to logarithmic terms, even though the potential remains smooth. It is concluded (i) that the nonexistence of polynomial expansions near bifurcation points of higher order, recently reported by several authors, does not imply the nonexistence of a smooth potential, and (ii) that even in cases where the Hamilton-Jacobi equation has a particular solution in the form of a power series, that particular solution may still fail to represent the nonequilibrium potential by failing to satisfy the necessary boundary condition at the attractor.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics