Thermodynamics behind Deliquescence?
The vapour pressure lowering is a consequence of Raoult's law with a non-volatile solute, i.e. a solvent that has zero vapour pressure (or at least, lower vapour pressure than the solvent).

Regarding the second part (“How can we derive, understand or quantify various thermodynamic parameters (ΔG,ΔS,ΔH etc) for the process of deliquescence?”), I am not sure exactly what you are looking for. This is a complex phenomenon, and there is a lot of research literature of the topic. To give only one example, see


  “Water-Solids Interactions: Deliquescence”, Lisa J. Mauer and Lynne S. Taylor, Ann. Rev. of Food Sci. Technol., 2010, 1, 41-63.