This paper presents an integrative dynamic model of Colombian population distribution, grounded in the maximum entropy principle and the flow of matter, energy, and information. The authors explore the interactions between human society and natural systems, focusing on the exchange of information, matter, and energy. The human population is presented as a convergence variable of these three physical entities, and a population distribution model for Colombia is developed using the maximum entropy principle to integrate the balances of related variables as macro-state restrictions. The selected variables include electrical consumption, water demand, and higher education rates (energy, matter, and information). The model includes statistical moments for previous population distributions and is shown to predict yearly population distribution by combining these variables, allowing for future dynamics exploration. The implications of this model contribute to bridging information sciences and sustainability studies. The paper discusses the conceptual framework, the construction of the model, and the results, highlighting the successful integration of an informational variable into the model. The model demonstrates a causal relationship between population dynamics and the defined variables, with statistical moments improving the accuracy of population distribution predictions. The authors suggest that the model can be useful for resource management and regional planning, but further research is needed to refine the model and explore its potential in different contexts.This paper presents an integrative dynamic model of Colombian population distribution, grounded in the maximum entropy principle and the flow of matter, energy, and information. The authors explore the interactions between human society and natural systems, focusing on the exchange of information, matter, and energy. The human population is presented as a convergence variable of these three physical entities, and a population distribution model for Colombia is developed using the maximum entropy principle to integrate the balances of related variables as macro-state restrictions. The selected variables include electrical consumption, water demand, and higher education rates (energy, matter, and information). The model includes statistical moments for previous population distributions and is shown to predict yearly population distribution by combining these variables, allowing for future dynamics exploration. The implications of this model contribute to bridging information sciences and sustainability studies. The paper discusses the conceptual framework, the construction of the model, and the results, highlighting the successful integration of an informational variable into the model. The model demonstrates a causal relationship between population dynamics and the defined variables, with statistical moments improving the accuracy of population distribution predictions. The authors suggest that the model can be useful for resource management and regional planning, but further research is needed to refine the model and explore its potential in different contexts.