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 for download.

We recommend running these programs as a stand-alone application (a jar file) from the Launcher. The latter includes all the STP programs. You can also download individual simulations, but their names do not always correspond with the names of the programs in the text.

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 the texts such as Harvey Gould and Jan Tobochnik, Statistical and Thermal Physics, Princeton University Press (2010) or Daniel
Schroeder, *An Introduction to Thermal Physics,* Addison-Wesley
(2000). The Gould/Tobochnik text is also available online and be freely downloaded.

**Approach to equilibrium**. Explore some of the qualitative properties of macroscopic systems.**Simple Monte Carlo simulation**. A Monte Carlo simulation of noninteracting particles initially confined to one half of the box.**Three partitions**. A molecular dynamics simulation of a Lennard-Jones fluid initially confined in the middle third of the simulation cell.**Two partitions**. A molecular dynamics simulation of a Lennard-Jones fluid initially confined to half of the simulation cell.

**An ideal thermometer**. Why is an extra degree of freedom called the demon an ideal thermometer?**Ideal gas**. The demon exchanges energy with an ideal gas. Illustrates that the demon can be interpreted as a thermometer.**Einstein solid**. The demon exchanges energy with an Einstein solid. Illustrates a universal property of the demon.**Lennard-Jones fluid**. Simulation shows the relation of the temperature as determined by the demon and the mean kinetic energy per particle.

**Sensitivity to initial conditions**. A molecular dynamics simulation of a Lennard-Jones system in a specially prepared state.**Random walks**. What happens to a drunken sailor?**1D random walk**. One-dimensional walk (fixed step length).**1D random walk**. One-dimensional walk (variable step length).**2D random walk**. Two-dimensional random walk.**Self-avoiding walk**. A Monte Carlo simulation using an improved enrichment algorithm.

**Multiple coin toss**. Monte Carlo simulation of the statistical properties of the outcome of the tosses of many coins.**Binomial distribution**. The plots illustrate how the width and relative width depend on N, the number of steps.**Central limit theorem**. A demonstration of the probability distribution of a random additive process.**Monte Carlo estimation**. Estimation of the area under a curve using the "hit or miss" method.**A simple multiplicative random process**. The simulation illustrates the importance of rare events.**Boltzmann probability**. A Monte Carlo simulation of an ideal classical gas in one dimension in equilibrium with a heat bath.**Simple thermal interaction**. The number of states of two harmonic solids that can exchange energy. What quantity becomes equal?**The number of states for two Einstein solids that can exchange particles**. What quantity becomes equal?**An Einstein solid in equilibrium with a heat bath**. A simulation of an Einstein (harmonic) solid using the Metropolis algorithm.**Entropy and temperature**. Calculation of the entropy of two harmonic solids that can exchange energy.**Thermal equilibrium**. A molecular dynamics simulation of two solids in thermal contact. What quantity becomes the same in thermal equilibrium?**Lennard-Jones fluid**. 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.**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.**Ising model**.**1D Ising model**. A Monte Carlo simulation of the one-dimensional Ising model. Output includes mean energy and heat capacity.**2D Ising model**. A Monte Carlo simulation of the two-dimensional Ising model. Output includes the mean energy, heat capacity, and the susceptibility.**Simulation of the Ising antiferromagnet on a square lattice**.**Simulation of the Ising antiferromagnet on an hexagonal lattice**.**Mean-field solution**. Plot of the numerical solutions to the usual self-consistent equation and the corresponding free energy.**Density of states of the 2D Ising model**. A Monte Carlo estimation of the density of states using the Wang-Landau algorithm.**Partition function of the 2D Ising model**. A Monte Carlo estimate of the partition function using a novel algorithm.**Hysteresis**. Simulation of hysteresis in the two-dimensional Ising model.

**Ideal gas integrals****Ideal Bose gas**. Calculation of the chemical potential as a function of temperature for fixed density for an ideal Bose gas.**Ideal Fermi gas**. Calculation of the chemical potential as a function of temperature for fixed density. The calculated chemical potential is used to determine the mean energy.

**Number of states of a particle in a box**. A comparison of the actual number of states to the asymptotic expression.**Second virial coefficient**. A calculation of the temperature-dependence of the second virial coefficient for the Lennard-Jones potential.**Generalized demon algorithm**. A generalization of the demon algorithm that yields the chemical potential as well as the temperature.**Diffusive equilibrium**. A simulation of a lattice gas with different chemical potentials.**Chemical potential**. An estimation of the chemical potential of a Lennard-Jones fluid using the Widom insertion method**Potts model**. Application of the Wang-Landau algorithm to the q-state Potts model.**XY or planar model**. A simulation of the two-dimensional XY model. See the development of vortices below the Kosterlitz-Thouless transition.**Fermi-Pasta-Ulam problem**. Simulation of a chain of oscillators coupled by anharmonic springs.**Percolation**. The nature of the geometrical phase transition for site percolation on a square lattice is illustrated.**Coarse graining**. Demonstration of the renormalization group method in the context of site percolation.**Quantum Monte Carlo**. A Monte Carlo simulation of an ideal quantum gas in one, two, or three dimensions.**Diffusion on a lattice**. A simple Monte Carlo simulation of particles on a lattice with a maximum of one particle per site.

The programs were developed by Kipton Barros, Ranjit Chacko, Joshua Gould, Harvey
Gould, Natali Gulbahce, Peter Sibley, Jan Tobochnik, and Hui Wang. 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 4 August 2014.