English

General criterion for harmonicity

Statistical Mechanics 2017-10-11 v2

Abstract

Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a "perfect spring", namely a polymer with non-Gaussian, exponentially distributed sub-units which nevertheless remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.

Keywords

Cite

@article{arxiv.1703.00769,
  title  = {General criterion for harmonicity},
  author = {Karel Proesmans and Hans Vandebroek and Christian Van den Broeck},
  journal= {arXiv preprint arXiv:1703.00769},
  year   = {2017}
}
R2 v1 2026-06-22T18:33:35.886Z