Optimization of processes by equipartition

We examine the problem of energy-efficient production in industrial processes. By energy-efficient we mean minimum entropy production. We use the possibility to redistribute the production in different times or parts of the system for a given total production, and show that a distribution that equipartitions the derivative of the local entrpy production rate with respect to the local production minimizes the entropy production. Equipartition in time implies stationary state production. Equipartition in space implies production for a given position independent force. The same constant derivative of the entropy production rate is found if one optimizes the production for a given total entropy production. Close to equilibrium the equipartition condition is found to reduce to the isofrce principle. Further from equilibrium, this reduction is extended to a whole class of non-linear flux-force relations. We show that, when one increases the total production, the entropy production per unit produced starts to increase linearly, as a function of this total production. It is shown which process conditions give an optimum path with an equipartition of the entropy production rate. How this relates to the isoforce principle is dicsussed. In general constraints on the process restrict the freedom to optimize, and therefore make it possible to realize the most favorable conditions. The importance of The Onsager relations for the systematic description of the optimization is discussed.