where we define the b solute-solvent entropy as ∆ b S b,V ≡ -k B ln⟨e +βδ1V b,V ⟩ 1 , which is the analog to the total solute-solvent entropy, S U,V , introduced in Eq. 15. By the same reasoning as is presented in Ref. 29, Eqs. 21 and 22 demonstrate that upon turning on the b-V interactions with the solute and solvent already coupled via the corresponding a interactions, the total reorganization energy and entropy exactly cancel: