Relating physics of multicomponent phase separation to computational abilities

Establish how the physics of multicomponent phase separation determines computational abilities such as expressivity, capacity, and decision-boundary sharpness.

Background

The article introduces computational metrics for classification by physical systems—sharpness of decision boundaries, capacity (number of distinct outputs), and expressivity (range of computable input-output maps). For neural networks, architectural features are known to control these metrics.

In contrast, for multicomponent phase separation, the connection between physical determinants (e.g., interaction matrices, ensemble constraints, kinetics) and computational performance remains unresolved. Clarifying this mapping is essential for assessing the feasibility and design space of phase-separation-based computation.