Intertheoretical relationships based on three-model framework

Intertheoretical relationships have been traditionally investigated through the notions of reduction and emergence. Recently, the focus has shifted towards the relationship between models for elaborating intertheoretical relationships in physics. This article demonstrates that three, rather than two, types of models are essential for elucidating some intertheoretical relationships. Beyond the conventional higher- and lower-level models, an intermediate-level model is crucial for establishing connections between the theories. This framework is not only applicable to some practical cases but also effectively captures the characteristics of two significant intertheoretical relationships: between classical and quantum mechanics, and between thermodynamics and statistical mechanics. By applying this framework to these cases, this study highlights both the similarity and the difference in these intertheoretical relationships.