2345 Although these approaches offer value, they share a common limitation: none explicitly incorporates the concept of overlapping possible futures, understood as the simultaneous coexistence of multiple preventative configurations before the materialization of an event. A similar conceptual framework can be found in: • Intrinsically Safe Design (ISI). • Early hazard identification (EN-HazID) in process engineering. • Models of complex systems in aviation and petrochemicals. • Advanced “leading indicators” approaches. However, none of them formalize the representation of simultaneous potential states. The QPIFAT seeks to fill this methodological gap. At the industrial level, fatigue management relies on work-rest rules, physiological monitoring, statistical analysis of alarms, and probabilistic models. While these approaches offer value, none formalizes the simultaneous coexistence of multiple possible futures before an event occurs, nor does any structuredly integrate latent and human variables within an anticipatory framework. 4. FOUNDATIONS OF QPIFAT The Quantum Potential Index Applied to Fatigue is a conceptual model inspired by principles of quantum physics, used metaphorically to represent the behavior of complex organizational systems. The use of the term “quantum” does not imply the direct application of quantum mechanical equations but rather serves as an analogy to describe the coexistence of multiple possible operational futures before an event occurs. The model is based on two fundamental conceptual principles: 4.1 Overlap of states Before an event materializes, the operating system can simultaneously exist in multiple potential configurations. Each of these configurations possesses a distinct level of operational energy, systemic tension, and materialization potential, even though not all are directly observable through traditional indicators.($!,$#,…,$$) From this perspective, fatigue is not manifested solely as a single event, but as a result of the dynamic interaction of multiple variables that coexist in the system before its explicit manifestation. 4.2 System collapses due to decision or condition When the operation selects a specific course of action, or when a critical condition occurs (for example, a high-severity fatigue alert), the system collapses into a single observable state. At this point, the event ceases to be potential and becomes part of operational history. The QPIFAT is geared towards observing and quantifying the system before this collapse, when it is still possible to intervene in a preventive and less disruptive way. The QPIFAT proposes to represent potential states using: • Observable precursor variables (O): frequency and severity of fatigue alerts, recurrence rates, operational response times. • Latent variables not directly measurable (L): Trends in accumulated fatigue, operational pressure, actual effectiveness of recovery actions. • Dynamic human factors (H): level of experience, overtime, rotation patterns and shift adaptation. • Environmental and energy conditions (E): night operation, visibility, presence of water, track geometry and physical-environmental condition of the cabin (vibration, temperature, dust and noise).
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