Computer Simulation Approach to Teaching Fundamental Ideas in Statistical Physics

Microscopic description of a system of classical particles in terms of their positions and velocities as a function of time is generated using Verlet algorithm in Scilab. The interactions between the particles are modeled according to Leonard Jones potential. The histograms of speeds and velocities are plotted by considering various time frames of simulation as constituting the ensemble. The distributions obtained are found to be similar to those of the macroscopically suggested Maxwell-Boltzmann distribution, validating the simulation procedure. Next, by assuming the state of each particle in the system to be described by whether that particle is on the left or right hand side of the box, the relationship between entropy and the number of microstates for an isolated, isothermal system at equilibrium is deduced.