Thermodynamics of the harmonic oscillator using coherent states

TL;DR

This paper explores how thermodynamic properties of a quantum harmonic oscillator can be derived from quantum states, demonstrating the importance of coherent states in connecting quantum and classical results.

Contribution

It shows that populating the Hilbert space with coherent states is essential to recover classical thermodynamic behavior from quantum dynamics.

Findings

Coherent states bridge quantum and classical thermodynamics.

Proper phase space population reproduces classical results.

Quantum time evolution can yield thermodynamic properties.

Abstract

The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the Hilbert space or an appropriately defined phase space must be populated in terms of coherent states in order to obtain the quantum result respectively the classical one.