Fluxes and the elimination of fast-relaxing variables

The behavior of fluxes under elimination of fast-relaxing variables from linear dynamical evolution equations is investigated. It is found that the fluxes corresponding to evolution equations which result from eliminations do not in general yield an adequate representation of the fluxes corresponding to the evolution equations from which the variables have been eliminated. In all examples considered, a discrepancy occurs when the eliminations reduce a cycle with nonzero thermodynamic force to a single state. The entropy production corresponding to the evolution equations resulting from the eliminations lacks terms corresponding to such cycles.