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A suitable coherent description of the reversible and irreversible magnetic entropy changes in a Tb-based metallic glass with strong random magnetic anisotropy (RMA) is presented. A giant irreversible positive magnetic entropy change is observed from magnetic measurements at low temperatures, which is found to arise from the entropy production, while a small negative one is obtained from heat capacity measurements. The temperature dependences of the irreversible positive magnetic entropy change under a field change of 5 T and the internal entropy production in the initial magnetization process can be described by an exponential law, which is determined by RMA.