Now I will evaluate if using Boltzmann rather than Bose-Einstein or Fermi-Dirac statistics is consistent by investigating if the chemical potential in Eqs. 4d and 4e can indeed be transferred to the partition function. First, I rewrite Eqs. 4d and 4e (Eq. 23a) and simplify for low occupation numbers (𝑝(𝑞) ≪ 1 ⇔ 𝜀(𝑞) -µ ≫ 𝓀 𝐵 𝑇). Now I can factor out the chemical potential (Eq. 23b) and use Eqs. 14c and 17a to obtain an equation for the partition function (Eq. 23c). Finally, combining Eqs. 23b and 23c leads to Eq. 23d. The chemical potential is defined as the change in extensive Gibbs free energy, 𝔾 = 𝐺 • 𝑁, when the number of elements 𝑁 changes. As no interactions between individual elements is considered, I can write this relationship in Eq. 23e and find an equivalent expression to Eq. 21c. This proves the consistency of applying Boltzmann statistics and ignoring the quantum effects at sufficiently low occupation numbers in the context of this work and gives a direct relationship between partition functions and the intensive Gibbs free energy (Eq. 23f). However, this result also suggests that the TST, as derived here, would not apply at small activation barriers as quantum effects cannot be ignored at higher occupation numbers, which I would estimate to be around 10 kJ/mol at standard conditions as 𝑒