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Since the discovery of long-time tails, it has been clear that Fourier's lawin low dimensions is typically anomalous, with a size-dependent heatconductivity, though the nature of the anomaly remains puzzling. Theconventional wisdom, supported by renormalization-group arguments andmode-coupling approximations within fluctuating hydrodynamics, is that theanomaly is universal in 1d momentum-conserving systems and belongs in theLevy/Kardar-Parisi-Zhang universality class. Here we challenge this picture byusing a novel scaling method to show unambiguously that universality breaksdown in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profilesfor a broad set of gradients, densities and sizes all collapse onto anuniversal master curve, showing that (anomalous) Fourier's law holds even deepinto the nonlinear regime. This allows to solve the macroscopic transportproblem for this model, a solution which compares flawlessly with data and,interestingly, implies the existence of a bound on the heat current in terms ofpressure. These results question the renormalization-group and mode-couplinguniversality predictions for anomalous Fourier's law in 1d, offering a newperspective on transport in low dimensions.

A violation of universality in anomalous Fourier's law