# Inverse temperature

It is often convenient to define a dimensionless *inverse* temperature, :

This notation likely comes from its origin as a Lagrangian multiplier, for which Greek letters are customarily written.

Indeed, it shown in Ref. 1 that this is the way it enters. The task is to maximize number of ways $N$ particles may be asigned to $K$ space-momentum cells. Introducing the partition function:

one could maximize its logarithm (a monotonous function):

where Stirling's approximation for large numbers has been used.

## References

- Kerson Huang, "Statistical Physics" John Wiley and Sons, second edition, pp. 79-85 (1987)