On a necessary criterion for stability of steady solutions of complex Ginzburg-Landau equation -- a counterexample to the 'maximum entropy production principle'

A maximum entropy production principle (MEPP) has been postulated to be a criterion of stability for steady states of open systems [Martyushev et al., Phys. Rep. 426, 1 (2006)]. We find a necessary condition for stability of steady solutions of the complex Ginzburg-Landau equation. This condition violates MEPP.