Introduction to soliton gas theory and generalised hydrodynamics
Thibault Bonnemain (LPTM, Cergy-Pontoise)
Generalised Hydrodynamics (GHD) is a rather recent theory that provides a framework for studying a wide family of many-body integrable and nearly integrable systems out of equilibrium. I will introduce the notion of soliton gas, associated with the Korteweg-de Vries (KdV) equation among others, and use it as a paradigmatic example for the GHD of integrable, classical field theories. In particular, by way of a heuristic argument based on the analogy between solitons and classical particles, I will construct the thermodynamics of the KdV soliton gas (free energy, entropy, static covariance…), as well as the Euler-scale hydrodynamic equations describing the evolution of weakly inhomogeneous gases. The results thus produced agree with numerical simulations; moreover they are consistent with and supplement the more rigorous, albeit less transparent, construction pioneered by Gennady El, based on the so-called thermodynamic spectral limit of finite-gap solutions.