Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems

TL;DR

This paper presents a universal method for identifying phase transition analogs in finite systems by analyzing inflection points in microcanonical entropy and inverse temperature, demonstrated on polymer transitions.

Contribution

It introduces a systematic classification approach based on microcanonical entropy inflections, applicable to any physical system and extendable to the thermodynamic limit.

Findings

Inflection points indicate cooperative activity and transitions.

Method successfully applied to polymer liquid-solid transitions.

Provides a general framework for finite system phase transition analysis.

Abstract

We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.