Integrated Collective Observables and the Loss of Mode Discrimination in Meso-Scale Systems

This technical note examines the limitations of integrated collective observables commonly used to characterize meso-scale physical systems. By isolating a minimal condition under which collective measurements collapse distinct internal mode configurations into identical outcomes, it shows how discriminative information may be lost despite locally informative responses. The analysis is purely diagnostic and non-theoretical, focusing on inferential limits imposed by collective measurement interfaces rather than on specific physical models or mechanisms.