To calculate free energies, experimental entropies were taken from thermochemical tables (Table ). Three approximations were made to fill gaps in available experimental entropy data for A x MnO 2 • yH 2 O phases. First, the difference in entropy between polymorphs with identical stoichiometry was assumed to be negligible. For example, the entropy of all pure MnO 2 structures was approximated as that of b-MnO 2 . Second, additional entropy arising from non-protonic ion insertion was assumed to be small, such that the entropy of A x MnO 2 (A ≠ H) was approximated as that of MnO 2 . Finally, the configurational entropies of intercalated H + and solvation shell H 2 O were assumed to be small so the entropies of H x MnO 2 • yH 2 O (0 < x < 1 & 1 < x < 2) were approximated as linear combinations of the entropies of b-MnO 2 , 𝛾-MnOOH, and 𝛿-Mn(OH) 2 according to the number of O-H bonds present (Fig. ). These approximations likely slightly underestimate the stability of A x MnO 2 • yH 2 O phases. However, we find that entropy accounts for approximately 10% or less of the free energy of Mn oxides at room temperature, consistent with previous work. Approximations made for unknown entropies are therefore unlikely to significantly affect our conclusions.