The G&G Model: A PDE Approach with Entropy and Irreversibility in Leadership and Policy Rehabilitation in the Democratic Republic of the Congo

This paper introduces the G&G Model with memory (Glody & Gilles Leadership Model), which uses a parabolic-to-pseudo-hyperbolic transition to investigate governance performances in the Democratic Republic of the Congo (DRC). The model inspired from Kurt Lewin’s field theory, formalizes how driving and restraining forces interact in social and political environment. The explicit inclusion of Shannon-type entropy as a source of disruption in the dissemination, interpretation, and implementation of public policies is a fundamental component of the model. While the shift to a pseudo-hyperbolic structure indicates the possibility of leadership stabilization, the parabolic model illustrates the irreversible nature of societal imbalances. For in depth accuracy to pinpoint crucial areas of instability or evolution, the model incorporates behavioral reactivity terms, impact gradients, and entropic components. This work provides a rigorous approach and lays the groundwork for mathematical modeling of governance and leadership, paving the way for further reform initiatives based on both quantitative analysis of intricate social systems and qualitative insight.