We consider walls connecting symmetric states in nonvariational one di
mensional spatially extended systems. We show that the problem can be
analyzed in terms of a free energy (nonequilibrium potential), which t
akes the same value in the asymptotic states (x -->+/-infinity). The m
otion of the walls can be understood as a residual dynamics on an exte
nded attractor in which the free energy takes a constant value.