The role of energy return on energy invested (EROEi) in complex adaptive systems

The energy return on energy invested, EROI or EROEI, is the ratio of the energy produced by a system to the energy expended to build, maintain, and finally dismantle the system. It is an important parameter for evaluating the efficiency of energy-producing technologies. In this paper, we examine the concept of EROEI from the general viewpoint of dynamic dissipative systems, providing insights on a wider range of applications. In general, natural resources can be assimilated to energy stocks characterized by a potential that can be exploited by creating intermediate stocks. This transformation is typical of dissipative systems and for the first time, we report that the Lotka- Volterra model, usually confined to the study of the biology of populations, can represent a powerful tool to estimate the EROEI of dissipative systems and, in particular, those systems subjected to depletion. This assessment is important to evaluate the ongoing energy transition since it provides us with a model for the decline of the EROEI in the exploitation of fossil fuels.