Revised Enskog equation for hard rods

Abstract

We point out that Percus's collision integral for one-dimensional hard rods [J. K. Percus, Physics of Fluids 12, 1560-1563 (1969)] does not preserve the thermal equilibrium state in an external trapping potential. We derive a revised Enskog equation for hard rods and show that it preserves this thermal state exactly. In contrast to recent proposed kinetic equations for dynamics in integrability-breaking traps, both our kinetic equation and its thermal states are explicitly nonlocal in space. Our equation differs from earlier proposals at third order in spatial derivatives and we attribute this discrepancy to the choice of collision integral underlying our approach.

v3: title updated, references added and revised for clarity. 8+3 pages

References in corpus (3)

• Transport properties of the classical Toda chain: effect of a pinning potential
• Unusual ergodic and chaotic properties of trapped hard rods
• Three-stage thermalisation of a quasi-integrable system

Cited by in corpus (8)

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• New classical integrable systems from generalized $T\bar{T}$-deformations
• Hamiltonian formulation and aspects of integrability of generalised hydrodynamics
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• Diffusive hydrodynamics of hard rods from microscopics
• Conserved densities of hard rods: microscopic to hydrodynamic solutions