Emergent phenomena in Nature: a paradox with Theory?

TL;DR

This paper explores the paradox of emergent phenomena like symmetry breaking and phase transitions occurring in finite quantum systems, which classical theories suggest should only appear in infinite limits, analyzing ideas bridging theory and real-world observations.

Contribution

It discusses mechanisms and ideas that reconcile the occurrence of emergent phenomena in finite quantum systems with theoretical expectations.

Findings

Finite quantum systems exhibit symmetry breaking and phase transitions.

The paper proposes mechanisms bridging theory and real-world phenomena.

It analyzes the paradox of emergence in physical systems.

Abstract

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 for 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 apparently ``paradoxical'' phenomena and outline various ideas and mechanisms that encompass both theory and reality, from physical and mathematical points of view.