Suppose the potential energy of a gas of point charges with positions and free to move on the infinite line , is given by
5.20.1 | |||
The probability density of the positions when the gas is in thermodynamic equilibrium is:
5.20.2 | |||
where is the Boltzmann constant, the temperature and a constant. Then the partition function (with ) is given by
5.20.3 | |||
See (5.14.6).
For charges free to move on a circular wire of radius ,
5.20.4 | |||
and the partition function is given by
5.20.5 | |||
See (5.14.7).
For further information see Mehta (2004).