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The influence of dynamics and sample shape on the magnetic hysteresis in first-order magnetocaloric metamagnetic LaFe13- xSi x with x = 1.4 is studied. In solid-state magnetic cooling, reducing magnetic and thermal hysteresis is critical for refrigeration cycle efficiency. From magnetization measurements, it is found that the fast field-rate dependence of the hysteresis can be attributed to extrinsic heating directly related to the thickness of the sample and the thermal contact with the bath. If the field is paused partway through the transition, the subsequent relaxation is strongly dependent on shape due to both demagnetizing fields and thermal equilibration; magnetic coupling between adjacent sample fragments can also be significant. Judicious shaping of the sample can both increase the onset field of the ferromagnetic-paramagnetic (FM-PM) transition but have little effect on the PM-FM onset, suggesting a route to engineer the hysteresis width by appropriate design. In the field-paused state, the relaxation from one phase to the other slows with increasing temperature, implying that the process is neither thermally activated or athermal; comparison with the temperature dependence of the latent heat strongly suggests that the dynamics reflect the intrinsic free energy difference between the two phases. [ABSTRACT FROM AUTHOR]