A thermodynamic explanation of the function of bifurcated structures in nature and in engineered artefacts

Why do bifurcated structures appear? In living and non-living systems, the construction of a bifurcation requires some energy input, and the 'economic principle' of nature suggests that this be justified by a compensating gain for the resulting structure. If the purpose of bifurcations is to transport material and immaterial flows, what underlying principle governs the radius ratio between branches, the diameter/length ratio, and the splitting angle? Do the prevailing boundary conditions influence their onset? This paper presents a novel thermodynamic model based on the assumption that the driving force behind the emergence of a bifurcation is its exergy cost. This is an extension and a completion of the Hess-Murray law: extension, because it measures the advantage of branched structures with respect to their non-branched counterparts in terms of exergy; completion, because it includes the 'formation exergy' neglected by previous theories. The model leads to a quantification of this primary exergy cost.