Enej Ilievski: Exact thermodynamics in classical soliton systems

Utilizing the machinery of algebraic integrability, I will discuss how to compute exact thermodynamic partition functions of classical soliton systems. Particularly, I will consider the paradigmatic case of the anisotropic Landau-Lifshitz theory, an integrable equation describing classical ferromagnetism in one spatial dimension. The equation of state, which physically describes a dense soliton gas, takes the form of a Fredholm integral equation -- the classical counterpart of thermodynamic Bethe Ansatz equations originally obtained for integrable quantum spin chains. Some of the lingering open problems will be highlighted as well.