Java Simulations for Statistical and Thermal Physics

The following programs were written for the Statistical and Thermal Physics curriculum development project and are part of the Open Source Physics project. The programs are released under the GNU General Public License. The source code is available.

You can run these programs as applets in a browser or download the Launcher as a stand-alone application (a jar file).

    The goal of the simulations and calculations is to illustrate some of the fundamental concepts in statistical mechanics. They can be used as standalone programs, or in conjunction with a text such as Daniel Schroeder, An Introduction to Thermal Physics, Addison-Wesley (2000), or in conjunction with the online notes by Harvey Gould and Jan Tobochnik.

    The programs were developed by Kipton Barros, Joshua Gould, Harvey Gould, Natali Gulbahce, Peter Sibley, Jan Tobochnik, and most recently by Hui Wang and Ranjit Chacko.

  1. Approach to Equilibrium. Explore some of the qualitative properties of macroscopic systems.
  2. An ideal thermometer. Why is an extra degree of freedom called the demon an ideal thermometer?
  3. Sensitivity to initial conditions. A molecular dynamics simulation of a Lennard-Jones system in a specially prepared state.
  4. Random walks. What happens to a drunken sailor?
  5. Multiple coin toss. Monte Carlo simulation of the statistical properties of the outcome of the tosses of many coins.
  6. Binomial distribution. The plots illustrate how the width and relative width depend on N, the number of steps.
  7. Central limit theorem. A demonstration of the probability distribution of a random additive process.
  8. Monte Carlo estimation. Estimation of the area under a curve using the "hit or miss" method.
  9. A simple multiplicative random process. The simulation illustrates the importance of rare events.
  10. Boltzmann probability. A Monte Carlo simulation of an ideal classical gas in one dimension in equilibrium with a heat bath.
  11. Simple thermal interaction. Calculation of the number of states of two harmonic solids that can exchange energy.
  12. Einstein solid at temperature T. Simulation of Einstein (harmonic) solid in equilibrium with a heat bath at temperature T using the Metropolis algorithm.
  13. Entropy and temperature. Calculation of the entropy of two harmonic solids that can exchange energy.
  14. Thermal equilibrium. A molecular dynamics simulation of two solids in thermal contact. What quantity becomes the same in thermal equilibrium?
  15. Lennard-Jones potential. A molecular dynamics or Monte Carlo simulation of a liquid in two dimensions. Output includes the mean pressure, temperature, heat capacity, and the radial distribution function.
  16. Hard disks. A molecular dynamics or Monte Carlo simulation of hard disks. Output includes the mean pressure, the mean free path, and the mean collision time.
  17. Ising model.
  18. Ideal gas integrals
  19. Number of states of a particle in a box. A comparison of the actual number of states to the asymptotic expression.
  20. Second virial coefficient.
  21. Generalized demon algorithm. A generalization of the demon algorithm that yields the chemical potential as well as the temperature.
  22. Ising lattice gas. A simulation of a lattice gas with different chemical potentials.
  23. Chemical potential. An estimation of the chemical potential of a Lennard-Jones fluid using the Widom insertion method
  24. XY or planar model. A simulation of the two-dimensional XY model. See the development of vortices below the Kosterlitz-Thouless transition.
  25. Fermi-Pasta-Ulam problem. Simulation of a chain of oscillators coupled by anharmonic springs.
  26. Percolation. The nature of the geometrical phase transition for site percolation on a square lattice is illustrated.
  27. Quantum Monte Carlo. A Monte Carlo simulation of an ideal quantum gas in one, two, or three dimensions.
  28. Diffusion in a solid. A simple Monte Carlo simulation of particles on a lattice with a maximum of one particle per site.

The Open Source Physics Java code library is described in Wolfgang Christian, Open Source Physics: A User's Guide with Examples, © Addison-Wesley, 2007.

Updated 13 May 2008.