Recently, the statistical physics modeling found a great success in the description of various aspects of adsorption phenomena such as olfaction, depollution, and photovoltaic processes. Therefore, we attempted here to apply this treatment in the domain of refrigeration by an adsorption/ desorption process cycle, using the grand canonical formalism of the statistical physics as a working tool. So, for this study, four advanced equations based on statistical physics treatment are used to clarify the adsorption process at molecular level and define its physico-chemical parameters for refrigeration applications. Our results showed that the double layer model with two energies provides useful details concerning this phenomenon by determining the number of captured HFO-1234ze (E) (C3H2F4) molecules per site nAM, the density of receptor site Drs, the adsorption quantity at saturation N a sat and two energetic parameters Phs1 and Phs2. The steric results revealed that the adsorbed C3H2F4 molecules tended towards a parallel position when the temperature increased. Evaluations of the adsorption energies and enthalpy values indicated that the anchoring process is exothermic and of a physisorption nature. In order to improve the thermodynamic efficiency, the coefficient of performance was calculated by analyzing changes in thermodynamic functions, giving a value of 0.58 for the C3H2F4 / Maxsorb III. Also, the COP value can be enhanced by using the same adsorbate with high compressibility to minimize the machine size but changing the present adsorbent by activated carbon derived from biomass such as: Waste Palm Trunk (WPT-AC) and Mangrove wood (M−AC).