Alain Decoster 2004 J. Phys. A: Math. Gen. 37 9051 doi:10.1088/0305-4470/37/39/001
Variational principles and thermodynamical perturbations
Alain Decoster
Show affiliationsThermodynamical 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
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05.70.Ce Thermodynamic functions and equations of state
02.30.Xx Calculus of variations
- MSC
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37K55 Perturbations, KAM for infinite-dimensional systems
37D35 Thermodynamic formalism, variational principles, equilibrium states
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
- Subjects
- Dates
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Issue 39 (1 October 2004)
Received 15 March 2004, in final form 13 August 2004
Published 15 September 2004
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Variational principles and thermodynamical perturbations
Alain Decoster 2004 J. Phys. A: Math. Gen. 37 9051
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