Equipartition, optimal allocation, and the constructal approach to predicting organization in nature

Abstract

This is a review of recent engineering developments in thermodynamic optimization, which shed light on a universal design principle that accounts for macroscopic organization in nature. It is shown that the optimal performance of a finite-size system with purpose is always characterized by the equipartition of driving forces or the optimal allocation of material subject to overall constraints. Examples are drawn from natural inanimate systems (river basins, turbulent flow) and animate systems (living trees). It is shown that this principle also governs the architecture of tree networks. Tree networks can be obtained in purely deterministic fashion by minimizing the flow resistance (or the time of travel) between one point and a finite area or a finite volume (an infinite number of points). The shape of each volume element can be optimized for minimal flow resistance. The network is ‘constructed’ by assembling the shape-optimized building blocks, and proceeding in time from the smallest volume element toward larger constructs. In constructal theory small size and shapeless flow (diffusion) come first, and larger sizes and geometrical form (channels, streams) come later.