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Program TwoPartsMD models the behavior of particles moving in a two-dimensional box interacting through the Lennard-Jones potential. The motion evolves using the numerical solution of the differential equations in Newton's second law. The velocity Verlet algorithm is used to update the positions and velocities of the particles. Periodic boundary conditions are used so that particles that leave the box enter on the other side, much like many video games. Initially, all the particles are located in the left half of the box. The macroscopic quantity of interest is the number of particles in the two parts of the box. The goals of this simulation are to explore the approach to equilibrium, the nature of the fluctuations in equilibrium, and macroscopic irreversibility, even though the microscopic motion is reversible.

Problem: Approach to equilibrium

Program TwoPartsMD initially divides the box into two parts rather than three. Run the program and verify that the simulation shows similar qualitative behavior to that found using Program ThreePartsMD. Explain the use of toroidal boundary conditions.

Resource

Problem 1.1 in Statistical and Thermal Physics: With Computer Applications, 2nd ed., Harvey Gould and Jan Tobochnik, Princeton University Press (2021).