The complexity of armed conflicts is expressed in the number of fatalities that may span several orders of magnitude. This study presents a minimalist, physics-informed approach to estimating the likelihood of extreme conflict fatalities at the country level of analysis using Bayesian modeling and energy-based dynamics. Leveraging the Boltzmann distribution to construct a Dirichlet prior, we formulate a predictive measure that captures the underlying entropy and energy states of conflict severity. By analyzing a dataset of 112 countries in conflict, we support the predictive power of the proposed measure. The findings suggest that extreme conflict events may be better understood through a minimal but theoretically grounded approach.