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Direct studies of the adiabatic temperature change (ΔTad) in the Ni47Mn40Sn12.5Cu0.5 Heusler alloy in steady magnetic fields up to 8 T by the extraction method and in pulsed magnetic fields up to 50 T were carried out in this paper. The alloy Ni47Mn40Sn12.5Cu0.5 demonstrates a magnetostructural phase transition (MSPT) of the first order in the 254–283 K temperature range as well as a second order phase transition near the Curie temperature TC = 313 K. An inverse magnetocaloric effect (MCE) was found in the region of the MSPT, and it reaches the maximum value ΔTad = −12 K in 20 T at the initial temperature T0 = 275 K. The irreversible part of the MCE reached ΔTir = −10 K when the field is completely removed. We consider the dynamics of the MCE in the vicinity of the MSPT and discuss the mechanisms that cause the giant irreversibility of the MCE as well as the possibilities of its application in hybrid cooling systems. [ABSTRACT FROM AUTHOR]