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We review first how properties of curved surfaces can be studied using Hill'sthermodynamics, also called nano-thermodynamics. We proceed to show for thefirst time that Hill's analysis is equivalent to Gibbs for curved surfaces.This simplifies the study of surfaces that are curved on the nano-scale, andopens up a possibility to study non-equilibrium systems in a systematic manner.

Hill's nano-thermodynamics is equivalent with Gibbs' thermodynamics for curved surfaces