The molecular structure of bound layers at attractive polymer-nanoparticle interfaces strongly influences the properties of nanocomposites. Thus, a unifying theoretical framework that can provide insights into the correlations between the molecular structure of the bound layers, their thermodynamics, and macroscopic properties is highly desirable. In this work, molecular dynamics simulations were used in combination with local fingerprint analysis of configurational entropy and interaction energy at the segmental scale, with the goal to establish such physical grounds. The thickness of bound polymer layers is found to be independent of the polymer chain length, as deduced from density oscillations at the surface of a nanotube. The local configurational entropy of layers is estimated from pair correlations in equilibrium structures. By plotting mean layer entropy vs internal energy on a phase diagram, a one-to-one equivalence is established between the local structures of layers and their thermodynamic properties. Moreover, a gradient in local dynamics of segments in bound layers under equilibrium is observed normal to the nanoparticle surface. The relaxation times of individual layers show correspondence to their phase diagram fingerprints, thus suggesting that a unified perspective can be envisioned for such materials built on the grounds of locally heterogeneous interfaces.