## Friday, 14 January 2011

### Entropy and statistics

Entropy ~ a measure of the disorder of a
system.
A state of high order = low probability
A state of low order = high probability
In an irreversible process, the
universe moves from a state of low
probability to a state of higher
probability.
We will illustrate the concepts by
considering the free expansion of a gas
from volume Vi to volume Vf.
The gas always expands to fill the
available space. It never spontaneously
compresses itself back into the original
volume.
First, two definitions:
Microstate: a description of a system that
specifies the properties (position
and/or momentum, etc.) of each
individual particle.
Macrostate: a more generalized
description of the system; it can be in
terms of macroscopic quantities, such
as P and V, or it can be in terms of the
number of particles whose properties
fall within a given range.
In general, each macrostate contains a
large number of microstates.
An example: Imagine a gas consisting of
just 2 molecules. We want to consider
whether the molecules are in the left or
right half of the container.