Related Experiment Video
Updated: May 23, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Quantum statistics and thermodynamics in the harmonic approximation
J R Armstrong1, N T Zinner, D V Fedorov
1Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark.
Abstract:
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center-of-mass motion, and by counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters, and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method, which is considerably more computationally intensive.
Related Concept Videos
Calculation of First-Law Quantities II
Entropy and the Second Law of Thermodynamics
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy and the Second Law of Thermodynamics
Absolute Entropies and the Third Law of Thermodynamics
The Quantum-Mechanical Model of an Atom
Second Law of Thermodynamics
