Boltzmann entropy and the microcanonical ensemble

TL;DR

This paper modifies Boltzmann's entropy to better analyze phase transitions in finite systems, demonstrating a second order phase transition in a pendulum from vibrational to rotating states.

Contribution

It introduces a slight modification to Boltzmann's entropy enabling the study of phase transitions in finite systems.

Findings

Pendulum exhibits a second order phase transition.

Modified entropy effectively describes phase transition behavior.

Application to finite systems enhances understanding of phase transitions.

Abstract

Boltzmann's entropy is slightly modified to make it suitable for discussing phase transitions in finite systems. As an example it is shown that the pendulum undergoes a second order phase transition when passing from a vibrational to a rotating state.