Emergence as Phase Transition: A Unified Framework from Philosophical Redefinition to Biological Self-Organization

The concept of "emergence" has become pervasive across philosophy, complex
systems theory, and biology, yet suffers from fundamental definitional ambiguity.
Chalmers' influential distinction between "weak" and "strong" emergence fails to
provide operational criteria: weak emergence conflates computational intractability with
ontological novelty, while strong emergence lacks empirical instantiation. This paper
proposes a radical redefinition grounded in physics: emergence is the appearance of
a non-zero order parameter following symmetry-breaking phase transition at a
critical point. Using the Landau-Stuart equation as the canonical form, we
demonstrate that this framework provides measurable critical conditions, identifiable
order parameters, and traceable dynamics. Furthermore, we show that this
mathematical structure is isomorphic across scales—from Shimizu's molecular motor
theory (1972) to the Vicsek model of collective motion (1995) and Motility-Induced
Phase Separation (MIPS). By integrating the Free Energy Principle, we propose that
thermodynamic instability serves as the physical driver for exploration, enabling
systems to minimize variational free energy. This unified framework rescues
"emergence" from buzzword status and establishes it as a rigorous scientific concept
with predictive power across molecular, cellular, neural, and social scales.