  Glansdorff and Prigogine (1970) proposed a decomposition of the entropy
production rate, which today is mostly known for Markov processes as the
Hatano-Sasa approach. Their context was irreversible thermodynamics which,
while ignoring fluctuations, still allows a somewhat broader treatment than the
one based on the Master or Fokker-Planck equation. Glansdorff and Prigogine
were the first to introduce a notion of excess entropy production rate
$\delta^2$EP and they suggested as sufficient stability criterion for a
nonequilibrium macroscopic condition that $\delta^2$EP be positive. We find for
nonlinear diffusions that their excess entropy production rate is itself the
time-derivative of a local free energy which is the close-to-equilibrium
functional governing macroscopic fluctuations. The positivity of the excess
$\delta^2$EP, for which we state a simple sufficient condition, is therefore
equivalent with the monotonicity in time of that functional in the relaxation
to steady nonequilibrium. There also appears a relation with recent extensions
of the Clausius heat theorem close-to-equilibrium. The positivity of
$\delta^2$EP immediately implies a Clausius (in)equality for the excess heat. A
final and related question concerns the operational meaning of fluctuation
functionals, nonequilibrium free energies, and how they make their entr\'ee in
irreversible thermodynamics.
