The paper presents an analytical formulation for the thermodynamics, free energy, and entropy of a generic Bogoliubov-de Genes (BdG) model that exhibits exceptional points (EPs) in its complex spectrum when coupled to reservoirs. The authors apply this formalism to a non-Hermitian Josephson junction, where the supercurrent does not exhibit divergences at EPs, contrary to recent claims. Instead, the entropy shows a universal jump of \( \frac{1}{2} \log 2 \), which is linked to the emergence of Majorana zero modes (MZMs) at EPs. The method allows for precise analytical boundaries of temperatures at which such Majorana entropy steps appear. A generalized Maxwell relation is proposed, linking supercurrents and entropy, which could facilitate the experimental observation of these steps in quantum-dot-based minimal Kitaev chains. The paper also discusses the non-Hermitian minimal Kitaev Josephson junction, where the critical temperatures and entropy changes are calculated, and the physical significance of these results is illustrated through numerical simulations.The paper presents an analytical formulation for the thermodynamics, free energy, and entropy of a generic Bogoliubov-de Genes (BdG) model that exhibits exceptional points (EPs) in its complex spectrum when coupled to reservoirs. The authors apply this formalism to a non-Hermitian Josephson junction, where the supercurrent does not exhibit divergences at EPs, contrary to recent claims. Instead, the entropy shows a universal jump of \( \frac{1}{2} \log 2 \), which is linked to the emergence of Majorana zero modes (MZMs) at EPs. The method allows for precise analytical boundaries of temperatures at which such Majorana entropy steps appear. A generalized Maxwell relation is proposed, linking supercurrents and entropy, which could facilitate the experimental observation of these steps in quantum-dot-based minimal Kitaev chains. The paper also discusses the non-Hermitian minimal Kitaev Josephson junction, where the critical temperatures and entropy changes are calculated, and the physical significance of these results is illustrated through numerical simulations.