Praseodymium-based 1-2-20 cage compounds Pr$T_2X_{20}$ ($T$ is generally Ti, V, Nb, Ru, Rh, Ir; and $X$ is either Al, Zn or Cd) provide yet another platform to study non-trivial electronic states of matter ranging from topological and magnetic orders to unconventional multipolar orders and superconductivity. In this paper, we report measurements of the electronic heat capacity in two Pr-based 1-2-20 materials: PrNi$_2$Cd$_{20}$ and PrPd$_2$Cd$_{20}$. We find that the lowest energy multiplet of the Pr $4f^2$ valence configuration is a $Gamma_3$ non-Kramers doublet and can, therefore, be described as a two-level system. By analyzing the dependence of the energy splitting between the ground and first excited singlet states on external magnetic field, we found that the interactions between the two-level systems are weak in PrNi$_2$Cd$_{20}$. However, in PrPd$_2$Cd$_{20}$, the exchange interactions that ultimately promote magnetic or multipolar order are strong enough and must be taken into account to accurately describe the dependence of the energy level splitting on external magnetic field.
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