Hello, bonjour, geia sou, shalom.
Welcome to the second homework session
of Statistical Mechanics: Algorithms and Computations
from the Physics Department of the Ecole Normale Superieure.
The subject of this week is the simulation of hard disks.
The aim is twofold. First:
you will convince yourself
that the event-driven molecular dynamics
gives the same results for thermodynamics
as the direct sampling or the Markov chain Monte Carlo methods.
You will implement a simple example
for each method, compare the output,
and verify yourself the famous ergodic hypothesis.
Second, you will apply directly this three methods
event-driven molecular dynamics,
direct sampling and Markov chain
to study the phenomenology of hard disks.
You will observe that their finite radius leads to
unsuspected and surprising phenomenology.
For hard disks
each legal configuration has exactly the same probability,
but do not let this uniform probability distribution
mislead you to the assumption
that the actual behavior of the system will be uniform and boring.
As you will see in this homework, uniform probability distributions
can lead to surprisingly non-uniform results.
This is due to so called entropic forces
which we will study in more details next week.
They are everywhere in nature, be assured.
In the meantime, have fun with Homework session 2.