A violation of universality in anomalous Fourier's law

TL;DR

This paper demonstrates that the universality of anomalous Fourier's law in 1d momentum-conserving systems does not hold for the diatomic hard-point fluid, revealing a breakdown of previous theoretical predictions and providing a new understanding of heat transport.

Contribution

The study introduces a novel scaling method showing universality breakdown in 1d diatomic fluids, challenging established renormalization-group and mode-coupling theories.

Findings

Hydrodynamic profiles collapse onto a universal master curve.

Fourier's law remains valid deep into the nonlinear regime.

A bound on heat current in terms of pressure is established.

Abstract

Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Levy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profiles for a broad set of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier's law holds even deep into the nonlinear regime. This allows to solve the macroscopic transport problem for this model, a solution which compares flawlessly with data and, interestingly, implies the existence of a bound on the heat current in terms of pressure. These results question the renormalization-group and mode-coupling universality predictions for anomalous Fourier's law in 1d, offering a new perspective on transport in low dimensions.