2. Elements of Kinetic Theory

Ludwig Boltzmann

In a dilute gas the molecules are in free, linear flight most of the time; just occasionally their flight will be interrupted by a collision with a single other particle. The result of such an event, which in general may be treated as a classical elastic collision, is a change in the speeds and directions of both partners. So it should be possible to derive, from a

First he defined a **distribution density** such that
denotes the number of particles which at time
situated at and have a velocity .
The -dimensional space of the variables
has later been called `` space''.^{2.1}

The evolution in time of the function
is then described by
**Boltzmann's Transport Equation**. We will shortly sketch the derivation
and shape of this important formula.

A particularly important result of Boltzmann's equation is
its **stationary solution**, i.e. the function that
solves the equation in the long-time limit
.
It turns out that this **equilibrium distribution** in space
may be derived without explicitely solving the transport equation itself.
The strategy used to do so, called the
**method of the most probable distribution**, will be encountered
again in other parts of Statistical Mechanics.

- 2.1 Boltzmann's Transport Equation
- 2.2 The Maxwell-Boltzmann distribution
- 2.3 Thermodynamics of dilute gases
- 2.4 Transport processes
- 2.5 Just in case ...
- 2.6 Problems for Chapter 2

2005-01-25