  We consider the problem of constructing a thermodynamic theory of
non-equilibrium steady states as a formal extension of the equilibrium theory.
Specifically, studying a particular system, we attempt to construct a
phenomenological theory describing the interplay between heat and mechanical
work that takes place during operations through which the system undergoes
transitions between non-equilibrium steady states. We find that, in contrast to
the case of the equilibrium theory, apparently, there exists no systematic way
within a phenomenological formulation to describe the work done by the system
during such operations. With this observation, we conclude that the attempt to
construct a thermodynamic theory of non-equilibrium steady states in analogy to
the equilibrium theory has limited prospects for success and that the pursuit
of such a theory should be directed elsewhere.
