# Approach to Equilibrium: Problems

N interacting particles (default is 270) are arranged in the center third of a two-dimensional box.

1. What is the qualitative behavior of the number of particles in each third of the box (n1, n2, and n3) as a function of the time t? Does the system appear to show a direction of time? Is the direction of time better defined if the number of particles is large?
2. Suppose that we made a video of the motion of the particles considered in Problem 1. Would you be able to tell if the video were played forward or backward for the various values of N? Would you be willing to make an even bet about the direction of time? Does your conclusion about the direction of time become more certain as N increases?
3. How long does it take before the system appears to be in equilibrium? What is your criterion for equilibrium?
4. From watching the motion of the particles, describe the nature of the boundary conditions that are used in the simulation.
5. Run the system with N = 270 until t = 5. Then press the `Reverse` button, which reverse all the velocities, and continue the simulation. Does the system return to its initial state? Repeat for other times. Is there a time at which the system does not return to its initial state? Repeat for N = 27. What can you conclude about the N dependence of reversibility?

### Note:

Statistical and thermal physics problems by Harvey Gould and Jan Tobochnik are available online at <http://stp.clarku.edu/>.