Allometric scaling and maximum efficiency in physiological eigen time.

Abstract

General optimization results from physics indicate that maximum efficiency of a process, in the sense of minimum overall entropy production, is achieved when the rate of entropy production is constant over time, however not in ordinary clock time but on an, in general varying, "eigen time" scale, intrinsic to the system. We identify the eigen time of a biological system with "physiological time," which generally scales with the 1/4 power of body mass, M(1/4), over a vast range of species. Since it is equally well established that metabolic rate scales as M(3/4), it follows that organisms produce entropy at the same intrinsic rate, fulfilling a necessary condition for maximum efficiency, and are all, furthermore, equally efficient on the physiological eigen time scale.