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In this supplementary paper we present some details on the solid-liquidinterface detection, the deduction of the non-equilibrium free energy, theanalysis of the granular temperature and energy per mode, a validation of thesmall slope approximation, a description of the Langevin dynamics, and theerror analysis.

Supporting Material for: Capillary-like Fluctuations of a Solid-Liquid Interface in a Non-Cohesive Granular System