Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures

: "Every object that biology studies is a system of systems." (François Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but reshaped. Linking the properties of primitive components to the emergent behavior of composite networks remains a key open challenge. Here, we show that modular compositions generically decouple the spectral and Fiedler dimensions so that networks with identical thermodynamic exponents can exhibit parametrically different equilibration dynamics.