The present work is aimed at studying the computation of the thermodynamic potentials that describe the stability of anionic surfactant molecules in micellar aggregates. We report a set of molecular E dynamics simulations of a sodium octanoate micelle in aqueous solution using the umbrella sampling method along with the Jarzynski equality in order to compute the potential of mean force for the dissociation process of one surfactant molecule from a previously assembled micellar aggregate. The Jarzynski average was computed at several different temperatures in order to estimate the Gibbs energy of association for the octanoate anion, which was split into its enthalpic and entropic contributions. We also estimated the contributions arising from the polar head and the apolar tail for each thermodynamic potential, and a detailed picture emerged from these simulations. The aggregation is driven mostly by the Gibbs energy contribution arising from the hydrophobic tail, which was large enough to cancel out the unfavorable contribution from the polar head. Although the association process may be ascribed mostly to the transfer of the apolar tail to the micellar core, it should be noted that the polar head also contributed with a favorable entropic term to the overall Gibbs energy. These findings were rationalized by comparing the energetic and structural patterns of the hydration process of a free monomer in solution to an aggregated molecule. The interaction energy distributions presented at least two discernible populations and each population was related to a different structural pattern, as characterized by the radial distribution functions. Altogether, the changes in both the energy and structure of the hydration layer are consistent with the entropy-driven association of the surfactant into the micellar aggregate.