Why are hydrodynamic theories applicable beyond the hydrodynamic regime?

¹ Department of Physics, The Ohio State University, Columbus, Ohio 43210-1117, USA
² Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette, France
³ Department of Physics, Indian Institute of Science Education and Research (IISER), Homi Bhabha Road, Pashan, Pune 411008, India
⁴ Institute of Modern Physics Fudan University, 220 Handan Road, 200433, Shanghai, China
⁵ School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Jatni - 752050, India

^* e-mail: jaiswal.61@osu.edu
^** e-mail: jean-paul.blaizot@ipht.fr

Published online: 26 June 2024

Abstract

We present an alternative approach to deriving second-order nonconformal hydrodynamics from the relativistic Boltzmann equation. We demonstrate how constitutive relations for shear and bulk stresses can be transformed into dynamical evolution equations, resulting in Israel-Stewart-like (ISL) hydrodynamics. To understand the far-from-equilibrium applicability of such ISL theories, we investigate the one-dimensional boost-invariant Boltzmann equation using special moments of the distribution function for a system with finite particle mass. Our analysis reveals that the mathematical structure of the ISL equations is akin to that of moment equations, enabling them to approximately replicate even the collisionless dynamics. We conclude that this particular feature is important in extending the applicability of ISL theories beyond the hydrodynamic regime.