A many body system in equilibrium can be described by the rules of statistical mechanics. However, non-equilibrium situations are more ubiquitous in nature than equilibrium ones, and their general theory is not known. Hydrodynamics is one of the attempts to describe them. It is like a perturbation theory, with the zeroth order dynamics (also referred to as the Euler equations) obtained by assuming local equilibrium, and the first order dynamics (known as the Navier-Stokes equation) obtained by treating deviations from local equilibrium in a first order approximation. However, in certain situations, the first order terms may diverge, leading to a breakdown of the perturbation theory and thus of hydrodynamics itself. We will discuss such breakdown in a dipole-conserving fluid below four dimensions. Our discussion will be based on [1].
References:
[1] P. Glorioso, J. Guo, J. F. Rodriguez-Nieva and A. Lucas, Breakdown of hydrodynamics below four dimensions in a fracton fluid, Nature Physics (18), August 2022, 912-917.
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