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Coarsening dynamics is the process where a system in equilibrium exhibits a phase transition from a disordered high-temperature phase to an ordered low-temperature phase with a broken symmetry of the high-temperature phase, e.g., the Ising ferromagnet. After a sudden quench through the transition temperature, domains of the two competing ordered phases form and grow in time towards a new equilibrium state under the influence of the interfacial surface tension, which acts as a driving force for the domain growth. The domain morphology is statistically the same at all times when all distances are measured in units of R(t), a characteristic length scale (dynamical scaling).We review the equilibrium results [de la Rocha, A. R.; de Oliveira, P. M. C.; and Arenzon, J. J., Phys. Rev. E, 91, 042113 (2015)] for the Ising model of a recently introduced measure of the domain size heterogeneity [Lee, H. K.; Kim, B. J.; and Park H., Phys. Rew. E, 84, 020101 (2011), Jo, W. S.; Yi, S. D.; Baek, S. K.; and Kim, B. J., Phys. Rev. E, 86, 032103, (2012)]. Moreover, we generalize this observable to non-equilibrium conditions and follow it through the coarsening dynamics, which may shed some light on both the equilibrium and out-of-equilibrium properties of the Ising and Voter model.