The third law of thermodynamics, which states that the entropy approaches zero at the limit of absolute zero temperature, is recognized as one of the fundamental principles of thermodynamics. Recently, a quantum many-body phenomenon that violates the third law of thermodynamics has been theoretically proposed in cubic holmium (Ho) compounds [T. Hotta, J. Phys. Soc. Jpn. 90, 113701 (2021).]. This phenomenon, known as the multi-channel Kondo effect (MCK), occurs when the electronic spins in multiple conduction bands over-screen a local magnetic moment at an isolated magnetic ion. According to the theoretical calculations, if the ?5 triplet is the ground state of the crystalline electric field, MCK arises at zero magnetic field, and the magnetic entropy remains at log ? at 0 K, where ? = 1.61803… is the golden ratio. To demonstrate MCK, we are focusing on the cubic compounds HoTr₂Zn₂₀ (Tr = Co, Rh, Ir) as candidate materials. In my talk, I will primarily present the thermodynamic properties of the Tr = Co system.