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One puzzling phenomenon in glass physics is the so-called 'shadow glass transition'which is an anomalous heat-absorbing process below the real glass transition and influences glass properties.However,it has yet to be entirely characterized,let alone fundamentally understood.Conventional calorimetry detects it in limited heating rates.Here,with the chip-based fast scanning calorimetry,we study the dynamics of the shadow glass transition over four orders of magnitude in heating rates for 24 different hyper-quenched metallic glasses.We present evidence that the shadow glass transition correlates with the secondary(β)relaxation:(i)The shadow glass transition and the β relaxation follow the same temperature-time dependence,and both merge with the primary relaxation at high temperature.(ii)The shadow glass transition is more obvious in glasses with pronounced(3 relaxation,and vice versa;their magnitudes are proportional to each other.Our findings suggest that the shadow glass transition signals the thermodynamics of β relaxation in hyper-quenched metallic glasses.