Tafel-Butler effect on Entropy: In terms of thermodynamic properties, the overpotential directly impacts the entropy and enthalpy of the system. A lower overpotential, like 0.300 V, typically correlates with a more favorable entropy change during the reaction, as it implies less energy is wasted, leading to a more efficient process. The enthalpy of the reaction might also be slightly lowered, as the platinum active sites provide a better match for the reactants' electronic configurations, reducing the activation energy. In turn, the reaction proceeds more spontaneously, and the overall efficiency improves. The favorable thermodynamic conditions ensure that platinum-doped graphene can effectively catalyze electrophilic reactions, balancing the entropic and enthalpic contributions to promote the desired transformation with minimal energy loss. At a specific external pressure, such as 0.26667 Pa, the system reaches a state where the balance between the enthalpy change (ΔH) and the entropy change (ΔS) results in a stable value for the Gibbs free energy. The enthalpy term, representing the heat released during the reaction, becomes more significant at higher pressures, causing the reaction to release more energy. As a result, the Gibbs free energy, reaches a point where the exothermic nature of the system counteracts any entropy-driven changes. In conclusion, the entropy of the system impacts the HER rate positively.