This document introduces the Metabolism of Trust in Complex Systems: a theoretical and operational framework that reinterprets trust not as a technical certificate to be demonstrated, nor as a relational bond to be assumed, but as a living process endowed with rhythms, pathologies and thermodynamic balance. The framework integrates biology, complexity, thermodynamics and systems theory to offer a regulatory system applicable to industrial, energy, digital and community infrastructures. A model of six vital functions is proposed — production, consumption, circulation, immune system, measurement, controlled failure — and the energy dimension is identified as an objective criterion of metabolic health. The document finally proposes a radical thermodynamic criterion: sustainable trust is low-consumption trust.