Becoming Large, Becoming Infinite: The Anatomy of Thermal Physics and Phase Transitions in Finite Systems

TL;DR

This paper analyzes the structure of thermodynamics and statistical mechanics in finite systems, defining phase transitions as incipient singularities and exploring their implications for reduction and emergence.

Contribution

It introduces a new perspective on phase transitions in finite systems using renormalization group and finite-size scaling, clarifying the role of the thermodynamic limit.

Findings

Phase transitions are represented as incipient singularities in finite systems.

A definition of large but finite systems is provided.

Implications for reduction and emergence in critical phenomena are discussed.

Abstract

This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of reduction and emergence.