  We compare two approaches to nonequilibrium thermodynamics, the two-generator
bracket formulation of time-evolution equations for averages and the
macroscopic fluctuation theory, for an isothermal driven diffusive system under
steady state conditions. The fluctuation dissipation relations of both
approaches play an important role for a detailed comparison. The nonequilibrium
Helmholtz free energies introduced in these two approaches differ as a result
of boundary conditions. A Fokker-Planck equation derived by projection operator
techniques properly reproduces long range fluctuations in nonequilibrium steady
states and offers the most promising possibility to describe the physically
relevant fluctuations around macroscopic averages for time-dependent
nonequilibrium systems.
