Remarks about the Phase Transitions within the Microcanonical description

TL;DR

This paper discusses the nature of phase transitions in the microcanonical ensemble, emphasizing ergodicity breaking and suggesting a new perspective on topological changes related to system dynamics in the thermodynamic limit.

Contribution

It proposes that microcanonically relevant phase transitions are linked to ergodicity breaking and introduces a new viewpoint on topological changes involving subsets of configurational space.

Findings

Microcanonical phase transitions involve ergodicity breaking.

Topological changes in configurational space are not directly linked to phase transitions.

Effective trapping in certain subsets of configurational space explains phase transition phenomena.

Abstract

According to the reparametrization invariance of the microcanonical ensemble, the only microcanonically relevant phase transitions are those involving an ergodicity breaking in the thermodynamic limit: the zero-order phase transitions and the continuous phase transitions. We suggest that the microcanonically relevant phase transitions are not associated directly with topological changes in the configurational space as the Topological Hypothesis claims, instead, they could be related with topological changes of certain subset A of the configurational space in which the system dynamics is effectively trapped in the thermodynamic limit N→∞.