Degree of coupling and its relation to efficiency of energy conversion

The phenomenological description of two coupled flows leads to a definition of their "degree of coupling". This dimensionless parameter, the absolute value of which lies between zero and unity, is a generalization of the coefficient of coupling used in the theory of electrical networks; it should serve as a basis of comparison between systems in which the nature of the flows and the forces are different. The efficiency of energy conversion, which is defined by means of the entropy production function of the system, depends on both the degree of coupling and the conditions of operation; but the maximum efficiency and the efficiency at maximum output are uniquely determined by the degree of coupling. The requirement for optimal matching of the load to the converter is essentially dictated by the degree of coupling. Reversible energy conversion (when the efficiency is unity) is a limit towards which only fully coupled systems can tend at infinitesimal rates of flow. No energy conversion occurs when a non-equilibrium state is maintained against its tendency to relax, without net flow taking place. The energy required for this is derived from a spontaneous coupled process. Nor does energy conversion occur when matter (or heat, etc.) is transferred in the absence of a gradient of concentration (or temperature, etc.). The energy expended is determined by the degree of coupling and the internal resistance of the system. In biological systems, the two characteristic functions of active transport are the maintenance of a concentration gradient and the level transfer of considerable amounts of water and solutes.