Traditional energy decomposition analysis (EDA) methods can provide an interpretive decomposition of non-covalent electronic binding energies. However, by definition, they neglect entropic effects and nuclear contributions to the enthalpy. With the objective of revealing the chemical origins of trends in free energies of binding, we introduce the concept of a Gibbs decomposition analysis (GDA) by coupling the absolutely localized molecular orbital treatment of electrons in non-covalent interactions with the simplest possible quantum rigid rotor-harmonic oscillator treatment of nuclear motion at finite temperature. The resulting pilot GDA is employed to decompose enthalpic and entropic contributions to the free energy of association of the water dimer, fluoride-water dimer, and water binding to an open metal site in the metal-organic framework Cu(I)-MFU-4l. The results show enthalpic trends that generally track the electronic binding energy and entropic trends that reveal the increasing price of loss of translational and rotational degrees freedom with temperature.