Emergent Theory for Constitutive Relations in Classical Defect Systems
Abstract
Optical, acoustic, hydrodynamic, and thermal defect systems are often studied by analogy with each other. This may indicate that we may find a emergent theory for constitutive relations of classical defect systems. Start with thermal systems, we put up with a bootstrap method to describe classical transport. We conjecture that Landau-Khalatnikov equation could provide heat constitutive relations when taking heat flux as order parameter. We show that the corresponding effctive Lagrangian has similar form of that of Wick-rotated complex scalar field theory at non-relativistic limit, and only in perfect conducting situation that this system is a canonical ensemble. We argue that our method could be generalized to other systems besides thermal ones. By analogy with ferroelectrics, we propose the thermal domain model, which is a conserved current XY model. Phase transition of the thermal system is qualitatively discussed in this model.
Cite
@article{arxiv.2504.06864,
title = {Emergent Theory for Constitutive Relations in Classical Defect Systems},
author = {Hongrui Xu},
journal= {arXiv preprint arXiv:2504.06864},
year = {2025}
}