Determine the relevance of dynamical symmetries to other forms of emergence

Determine whether dynamical symmetry (equivariance) is relevant to other forms of emergence that focus on enhanced controllability (e.g., causal emergence) and on whole–part relationships, beyond the hierarchical emergence mechanism established via symmetry-induced informational closure.

Background

The paper develops a theoretical framework showing that dynamical symmetries (group equivariance) generate informationally closed macroscopic variables and a hierarchy of emergent levels aligned with subgroup lattices. This provides a symmetry-based account of hierarchical emergence in objective dynamics and Bayesian belief updating.

The authors note that other strands of work investigate different notions of emergence, including those centered on enhanced controllability/causal emergence and whole–part relationships. They explicitly state that it remains an open question whether the symmetry-based mechanism articulated here is relevant to these other kinds of emergence.