Binding of two short peptides of sequences ASN-ASP-MET-PHE-ARG-LEU and LEU-LEU-PHE-MET-GLN-HIS and their bound complex structures is studied. Molecular dynamic simulations of the three structures around their respective minimum energy conformations are performed and a quasi-harmonic analysis is performed over the trajectories generated. The fluctuation correlation matrix is constructed for all C-alpha-atoms of the peptides for the full trajectory. The spring constant matrix between peptide C-alpha-atoms is obtained from the correlation matrix. Statistical thermodynamics of fluctuations, the energies, entropies, and the free energies of binding are discussed in terms of the quasi-harmonic model. Sites contributing to the stability of the system and presenting high affinity for binding are determined. Contribution of hydrophobic forces to binding is discussed. Quasi-harmonic approximation identifies the essential subspace of motions, the important interactions, and binding sites, gives the energetic contribution of each individual interaction, and filters out noise observed in molecular dynamics owing to uncorrelated motions. Comparison of the molecular dynamics results with those of the quasi-harmonic model shows the importance of entropy change, resulting from water molecules being liberated from the surfaces of the two peptides upon binding.