Grain growth in polycrystal, as a competitive process by curvature-driven grain boundary motion, is a topic of high theoretical interest in metallurgy and other scientific disciplines. Due to the complexity of local grain-environment heterogeneity, the theoretical description of statistical grain-growth behaviors, e.g., grain size and topology distribution, is still incomplete. During the past 70 years, mean-field and stochastic theories are two typical routes for understanding the normal grain-growth kinetics. However, there exists a significant divergence between these two approaches. As two ways for the same question, there must be connections between them. In this work, a thermodynamic dissipation-based framework is established to represent the geometrical correlation and stochasticity of grain growth, revealing the relationship between previous mean-field and stochastic theories. In addition, the present work also generates an approach of extending the mean-field or stochastic models to the Aboav-Weaire relation, which is the most sensitive characteristic of the local grain-environment heterogeneity. Combining the thermodynamic-based framework with Aboav-Weaire relations, the validity of different theories is effectively verified.

Key words: Grain growth, Mean-field theory, Stochasticity, Grain topology