Stationary Nonequilibrium States in Boundary Driven Hamiltonian Systems: Shear Flow

TL;DR

This paper studies stationary nonequilibrium states in boundary-driven Hamiltonian particle systems, demonstrating how specific wall reflection rules induce shear flow and comparing entropy production with phase space compression, supported by molecular dynamics simulations.

Contribution

It introduces deterministic boundary rules that generate shear flow in Hamiltonian systems and establishes a connection between entropy production and phase space volume change under these conditions.

Findings

Entropy production equals phase space compression when incident velocities are Maxwellian.

Simulations confirm the theoretical predictions of shear flow behavior.

The approach links microscopic dynamics with macroscopic hydrodynamic equations.

Abstract

We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by Maxwell demon ``reflection rules'' at the walls. These deterministic rules conserve energy but not phase space volume, and the resulting global dynamics may or may not be time reversible (or even invertible). Using rules designed to simulate moving walls we can obtain a stationary shear flow. Assuming that for macroscopic systems this flow satisfies the Navier-Stokes equations, we compare the hydrodynamic entropy production with the average rate of phase space volume compression. We find that they are equal when the velocity distribution of particles incident on the walls is a local Maxwellian. An argument for a general equality of this kind, based on the assumption of local thermodynamic equilibrium, is given. Molecular dynamic simulations of hard disks in a channel produce a steady shear flow with the predicted behavior.