Standard hydrodynamics describes fluids with conserved charges: energy, momentum, particle number. Zhang, Lv, and Huang (arXiv:2603.17794) extend this to fluids carrying intrinsic dilation charge — a quantity related to scale transformations.
In a conformal theory, the dilation current is conserved. In a nearly conformal theory — like the quark-gluon plasma produced in heavy-ion collisions — it is approximately conserved, and the degree of violation (the scale anomaly) controls new transport phenomena. The dilation charge relaxes and diffuses with its own conductivity, analogous to how spin charge relaxes with spin conductivity.
The most striking prediction is a gapped dilation excitation and the freezing out of long-wavelength sound modes. Below a certain wavelength, the usual sound waves of a fluid disappear because the dilation degree of freedom absorbs the energy that would otherwise propagate as sound. This is formally analogous to the freezing of superhorizon modes in cosmology — modes that stretch beyond the horizon stop oscillating. Here, modes that couple too strongly to dilation relaxation stop propagating.
In the nonrelativistic limit, the theory reduces to microstretch fluid dynamics — a framework developed for materials with internal microstructure (liquid crystals, granular media, biological tissues). The connection is not accidental: a material with internal degrees of freedom that dilate and contract is literally a fluid with dilation charge.
Scale symmetry is usually thought of as a high-energy abstraction. Here it becomes a hydrodynamic transport coefficient — measurable, viscous, and dissipative.