Long-range systems, (non)extensivity, and the rescaling of energies
Abstract
Systems with long-range interactions have seen a surge of interest in the past decades. In the wake of this surge, the use of a system size-dependent rescaling, sometimes termed “Kac prescription,” of the long-range pair potential has seen widespread use. An ad hoc modification of the Hamiltonian may make the energy extensive, but its physical justification and implications are a frequent source of confusion and misinterpretation. After all, in real physical N-body systems, the pair interaction strength does not scale with the number N of constituents. This article presents, at an introductory level, scaling arguments that provide a clear physical interpretation of the “Kac prescription” for finite systems as well as in the thermodynamic limit.
Fields of Study & Subjects
Statistical Mechanics and Entropy
Theoretical and Computational Physics
Advanced Physical and Chemical Molecular Interactions
Publication details
- Journal / source
- American Journal of Physics
- Volume
- 94
- Issue
- 10
- Pages
- 842–848
- Publication date
- 22 September 2026
- Language
- EN