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Related Concept Videos

Calculation of First-Law Quantities II01:24

Calculation of First-Law Quantities II

The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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 Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
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Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

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Related Experiment Video

Updated: May 23, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

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.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 3, 2012
PubMed
Summary

We present a new computational method for calculating thermodynamic properties of identical bosons and fermions using the harmonic approximation. This approach simplifies calculations for systems in external fields, offering a more efficient alternative to brute force methods.

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Last Updated: May 23, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Computational physics

Background:

  • Calculating thermodynamic quantities for quantum systems can be computationally intensive.
  • Existing methods may not efficiently handle identical bosons and fermions in external fields.

Purpose of the Study:

  • To develop an efficient method for computing thermodynamic quantities for identical bosons and fermions.
  • To utilize the harmonic approximation and canonical partition function for simplified calculations.

Main Methods:

  • Separating center-of-mass motion to count states based on symmetry and excitation energy.
  • Employing the canonical partition function, focusing on energies and degeneracies.
  • Deriving oscillator frequencies from realistic model parameters for the harmonic Hamiltonian.

Main Results:

  • The proposed method accurately computes thermodynamic quantities for systems in the harmonic approximation.
  • Numerical calculations in two dimensions show good agreement with a more computationally intensive brute force method.
  • The approach represents an effective interaction based on harmonic interactions.

Conclusions:

  • The developed method provides an efficient and accurate way to determine thermodynamic properties of quantum systems.
  • This technique offers a significant computational advantage over traditional brute force approaches.
  • The method is applicable to identical bosons and fermions in external confining fields.