Since 2020, the receptor-binding domain (RBD) of the spike protein of the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been constantly mutating, producing most of the notable missense mutations in the context of “variants of concern”, probably in response to the vaccine-driven alteration of immune profiles of the human population. The Delta variant, in particular, has become the most prevalent variant of the epidemic, and it is spreading in countries with the highest vaccination rates, causing the world to face the risk of a new wave of the contagion. Understanding the physical mechanism responsible for the mutation-induced changes in the RBD’s binding affinity, its transmissibility, and its capacity to escape vaccine-induced immunity is the “urgent challenge” in the development of preventive measures, vaccines, and therapeutic antibodies against the coronavirus disease 2019 (COVID-19) pandemic. In this study, entropy–enthalpy compensation and the Gibbs free energy change were used to analyze the impact of the RBD mutations on the binding affinity of SARS-CoV-2 variants with the receptor angiotensin converting enzyme 2 (ACE2) and existing antibodies. Through the analysis, we found that the existing mutations have already covered almost all possible detrimental mutations that could result in an increase of transmissibility, and that a possible mutation in amino-acid position 498 of the RBD can potentially enhance its binding affinity. A new calculation method for the binding energies of protein–protein complexes is proposed based on the entropy–enthalpy compensation rule. All known structures of RBD–antibody complexes and the RBD–ACE2 complex comply with the entropy–enthalpy compensation rule in providing the driving force behind the spontaneous protein–protein docking. The variant-induced risk of breakthrough infections in vaccinated people is attributed to the L452R mutation’s reduction of the binding affinity of many antibodies. Mutations reversing the hydrophobic or hydrophilic performance of residues in the spike RBD potentially cause breakthrough infections of coronaviruses due to the changes in geometric complementarity in the entropy–enthalpy compensations between antibodies and the virus at the binding sites.