Abstract. Thermodynamical perturbation theory provides a method for calculating the partition function or the free energy of a system from the properties of another system. The first-order perturbation takes advantage of inequalities such as the Gibbs–Bogoliubov inequality in classical mechanics and the Peierls and Bogoliubov inequalities in quantum mechanics, which are used in variational calculations. We present here sequences of inequalities which generalize the former ones; they can be presented as rearrangements of perturbation expansions, which provide exact bounds. As an example, the free energy of an anharmonic oscillator is calculated with the first two variational principles.

PACS numbers: 05.90.+m, 05.30.−d, 05.20.−y

Print publication: Issue 39 (1 October 2004)
Received 15 March 2004, in final form 13 August 2004
Published 15 September 2004