  Entropy might be a not well defined concept if the system can undergo
transformations involving stationary nonequilibria. It might be analogous to
the heat content (once called ``caloric'') in transformations that are not
isochoric (i.e. which involve mechanical work): it could be just a quantity
that can be transferred or created, like heat in equilibrium. The text first
reviews the philosophy behind a recently proposed definition of entropy
production in nonequilibrium stationary systems. A detailed technical attempt
at defining the entropy of a stationary states via their variational properties
follows: the unsatisfactory aspects of the results add arguments in favor of
the nonexistence of a function of state to be identified with entropy; at the
same time new aspects and properties of the phase space contraction emerge.
