English

Phase Transition in a Vlasov-Boltzmann Binary Mixture

Mathematical Physics 2015-05-13 v1 math.MP

Abstract

There are not many kinetic models where it is possible to prove bifurcation phenomena for any value of the Knudsen number. Here we consider a binary mixture over a line with collisions and long range repulsive interaction between different species. It undergoes a segregation phase transition at sufficiently low temperature. The spatially homogeneous Maxwellian equilibrium corresponding to the mixed phase, minimizing the free energy at high temperature, changes into a maximizer when the temperature goes below a critical value, while non homogeneous minimizers, corresponding to coexisting segregated phases, arise. We prove that they are dynamically stable with respect to the Vlasov-Boltzmann evolution, while the homogeneous equilibrium becomes dynamically unstable.

Keywords

Cite

@article{arxiv.0904.0791,
  title  = {Phase Transition in a Vlasov-Boltzmann Binary Mixture},
  author = {R. Esposito and Y. Guo and R. Marra},
  journal= {arXiv preprint arXiv:0904.0791},
  year   = {2015}
}
R2 v1 2026-06-21T12:48:20.451Z