When lower heat losses become more concentrated: Shannon entropy and Jensen–Shannon divergence in an anonymised renovation sequence

Renovation can reduce total heat losses while leaving a larger fraction concentrated in a smaller set of mechanisms. A percentage reduction alone does not describe this change in composition. This paper analyses five consistently reported loss categories across a baseline and five cumulative renovation packages in a confidential nonresidential building assessment. Roof, wall, openings, lower-floor and ventilation losses are normalised into compositions and examined using Shannon entropy, effective category count and Jensen–Shannon divergence. The sum of these gross loss categories decreases from 334.285 to 128.839 kWh/(m² year), a reduction of 61.458%. Ventilation losses decrease by 18.807%, but their share increases from 25.449% to 53.612%. Normalised five-category entropy falls from 0.9870 to 0.8256, while the effective category count falls from 4.897 to 3.777. The trajectory is not monotonic: the system-optimisation stage increases compositional evenness relative to the preceding state. Divergence from baseline is greatest at an intermediate package, not the final package, demonstrating that compositional distance is not a saving or performance score. Aggregation and category-removal diagnostics show that the endpoint shift is primarily a change in the ventilation-versus-envelope balance. The study provides a reproducible descriptive framework for understanding residual losses without interpreting information entropy as thermodynamic entropy or equating a large category share with an immediately achievable saving. Results are model-based and require airflow, operating and comfort evidence before they can inform a subsequent intervention.