Diffusive hydrodynamics of hard rods from microscopics
arXiv:2503.07794 · doi:10.21468/SciPostPhysCore.9.1.010
Abstract
We derive exact equations governing the large-scale dynamics of hard rods, including diffusive effects that go beyond ballistic transport. Diffusive corrections are the first-order terms in the hydrodynamic gradient expansion and we obtain them through an explicit microscopic calculation of the dynamics of hard rods. We show that they differ significantly from the prediction of Navier-Stokes hydrodynamics, as the correct hydrodynamics description is instead given by two coupled equations, giving respectively the evolution of the one point functions and of the connected two-point correlations. The resulting equations are time-reversible and reduce to the usual Navier-Stokes hydrodynamic equations in the limit of near-equilibrium evolution. This represents the first exact microscopic calculation showing how ballistic dynamics generates long-range correlations, in agreement with general results from the recently developed ballistic macroscopic fluctuation theory, and showing how such long range-correlations directly affect the diffusive hydrodynamic terms, in agreement with, and clarifying, recent related results.
34 pages, 6 figures
References in corpus (16)
- Ballistic macroscopic fluctuation theory
- Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
- Generalized hydrodynamics: a perspective
- Anomalous transport from hot quasiparticles in interacting spin chains
- Distinct universality classes of diffusive transport from full counting statistics
- Dynamical criticality of magnetization transfer in integrable spin chains
- Universal anomalous fluctuations in charged single-file systems
- Hydrodynamic gauge fixing and higher order hydrodynamic expansion
- Non-Gaussian diffusive fluctuations in Dirac fluids
- Diffusive hydrodynamics from long-range correlations
- Unusual ergodic and chaotic properties of trapped hard rods
- Revised Enskog equation for hard rods
- Thermalization and hydrodynamics in an interacting integrable system: the case of hard rods
- Hydrodynamic noise in one dimension: projected Kubo formula and how it vanishes in integrable models
- Hydrodynamic fluctuations of stochastic charged cellular automata
- Scaling limits of solitons in the box-ball system