  This study examines a new formulation of non-equilibrium thermodynamics,
which gives a conditional derivation of the ``maximum entropy production''
(MEP) principle for flow and/or chemical reaction systems at steady state. The
analysis uses a dimensionless potential function $\phi_{st}$ for
non-equilibrium systems, analogous to the free energy concept of equilibrium
thermodynamics. Spontaneous reductions in $\phi_{st}$ arise from increases in
the ``flux entropy'' of the system - a measure of the variability of the fluxes
- or in the local entropy production; conditionally, depending on the behaviour
of the flux entropy, the formulation reduces to the MEP principle. The inferred
steady state is also shown to exhibit high variability in its instantaneous
fluxes and rates, consistent with the observed behaviour of turbulent fluid
flow, heat convection and biological systems; one consequence is the
coexistence of energy producers and consumers in ecological systems. The
different paths for attaining steady state are also classified.
