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Burgers equation from nonthermal stationary states in nearly integrable gases

Paweł Lisiak, Maciej Łebek*, and Miłosz Panfil

  • *Contact author: maciej.lebek@fuw.edu.pl
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Phys. Rev. E 114, 024115 – Published 10 August, 2026

DOI: https://doi.org/10.1103/shbc-ggbj

Abstract

When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets altered when transport is investigated on top of long-lived nonthermal states. Remarkably, for states noninvariant under parity we find the Burgers equation arising in the hydrodynamic limit. We explicitly compute the diffusion constant and nonlinear advective coefficient of the Burgers equation using a variant of the Chapman-Enskog theory. We find an excellent agreement between our theory and numerical simulations of a simplified model of stochastic two-body collisions. Our conclusions are based only on Galilean invariance, existence of a small system-bath coupling parameter, and a small momentum exchange between the system and the bath particles during two-body scattering.

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Phys. Rev. E 114, 024115– Published 10 August, 2026
  • Received 12 January 2026
  • Revised 16 May 2026
  • Accepted 23 June 2026
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