The relationship between the evolution of the basal metabolic rate (BMR) and the evolution of mass estimated as body weight in complex organisms such as human beings show the association between dissipated energy and information recovered as material structure. In such a context, it is necessary to highlight that the metabolic rate estimated as the energy dissipated per unit of mass presents the same rate of change as the mechanical speed estimated as distance traveled per unit of time. We describe this as a logical equivalence that has consequences on the geometry of the system. Our study proposes to describe the relationships between BMR, body weight, and the geometry of these systems in the same way that relativistic mechanics describes the relationships between matter, speed, and the geometry of the space in which the variables of a physical system are defined. It is exactly the same mechanical description, but considering five dimensions instead of four. The concept of information density limit is decisive in this theoretical framework since it contributes to explaining the changes in the geometry of these systems, their order-chaos transitions, and their general holographic description.
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