Maximum entropy analysis of steady-state flow systems (and extremum entropy production principles)

Recently, the author gave a MaxEnt-based analysis of steady-state flow systems, using an entropy defined on the set of instantaneous fluxes through an infinitesimal fluid element (R.K. Niven, Phys. Rev. E, 80(2) (2009) 021113). The formulation is analogous to Gibbs' formulation of equilibrium thermodynamics, which expresses the effect of changes in entropy within and outside a system, but is here applied to the steady state of a non-equilibrium flow system. The analysis yields a potential function (negative Massieu function, analogous to a free energy) to be minimised; this in turn can be approximated by a maximum or minimum entropy production (MaxEP or MinEP) principle in different circumstances. In this study, a generic version of the derivation is first provided, encompassing three seemingly disparate formulations of equilibrium thermodynamics, and local and global steady-state flow systems. A new analysis of global flow systems is provided, which supersedes previous attempts by Dewar. The analysis leads into a discussion of the possibility and implications of a scale invariance condition for the application of MaxEnt to flow systems.