Classical Linear Harmonic Oscillators to Describe Thermodynamic Properties of Quantum Linear Harmonic Oscillators and Solids

TL;DR

This paper demonstrates that classical linear harmonic oscillators with temperature-dependent parameters can replicate the thermodynamic properties of quantum harmonic oscillators and solids, providing a classical approach to understanding quantum thermodynamics.

Contribution

It shows that classical oscillators with temperature-dependent properties can match the partition function of quantum oscillators, offering a new classical perspective on quantum thermodynamic behavior.

Findings

Classical oscillators with temperature-dependent parameters share the same partition function as quantum oscillators.

Mean square displacements differ among classical systems with various temperature dependencies.

Classical oscillators effectively describe thermodynamic properties of quantum systems and solids.

Abstract

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.