This study proposes an energy-based framework for exploring local variations around observed territorial configurations in Official Statistics. The observed distribution serves as the initial reference, without assuming equilibrium. A register-derived graph represents structural similarities between municipalities, while socio-economic composite indices are synthesised through Principal Component Analysis into a univariate external field. A Continuous Ising model and a Langevin-based procedure provide complementary stochastic exploration strategies. Simulated Annealing progressively limits exploration, favouring lower-energy configurations under each specification. Recorded energy trajectories and municipal deviations characterise the resulting ensembles. Conformal Prediction provides calibrated intervals whose widths and empirical coverage describe their relationship with fixed observed municipal values under repeated subsampling. The application to resident foreign population shares in North-East Italy yields simulated municipal averages close to the observed values, but substantially different calibrated interval widths between the two procedures. Comparisons across territorial groups reveal heterogeneous associations with socio-economic profiles, without a uniform ordering of interval widths between central and peripheral municipalities. The framework connects territorial interactions, socio-economic information, and stochastic variation within an exploratory analysis. Its contribution is to examine how nearby simulated alternatives relate to the observed configuration and to formulate hypotheses about territorial heterogeneity. Further applications and sensitivity analyses would assess the robustness of these interpretations.

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