# Emergent phenomena in Nature: a paradox with Theory?

September 21, 2022

The existence of various physical phenomena stems from the concept called
asymptotic emergence, that is, they seem to be exclusively reserved for certain
limiting theories. Important examples are spontaneous symmetry breaking (SSB)
and phase transitions: these would only occur in the classical or thermodynamic
limit of underlying finite quantum systems, since in finite quantum systems,
due to the uniqueness of the relevant states, such phenomena are excluded by
Theory. In Nature, however, finite quantum systems describing real materials
clearly exhibit such effects. In this paper we discuss these "paradoxical"
phenomena and outline various ideas and mechanisms that encompass both theory
and reality, from physical and mathematical perspectives.

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