Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems

TL;DR

This paper investigates how memory effects influence nonequilibrium transport in a deterministic Hamiltonian system of coupled cells, refining previous models by analyzing higher-order effects and external gradients through phenomenological balance equations.

Contribution

It introduces a refined theoretical framework incorporating memory effects and external gradients, extending prior linear-profile models for Hamiltonian transport systems.

Findings

Higher-order effects cause deviations from linear profiles.

Asymmetries in reflection probabilities influence heat and particle transport.

Numerical simulations support the phenomenological balance equations.

Abstract

We consider nonequilibrium transport in a simple chain of identical mechanical cells in which particles move around. In each cell, there is a rotating disc, with which these particles interact, and this is the only interaction in the model. It was shown in \cite{eckmann-young} that when the cells are weakly coupled, to a good approximation, the jump rates of particles and the energy-exchange rates from cell to cell follow linear profiles. Here, we refine that study by analyzing higher-order effects which are induced by the presence of external gradients for situations in which memory effects, typical of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a set of balance equations for the particle number and energy in terms of the reflection probabilities of the cell and solve it phenomenologically. Using this approximate theory we explain how these asymmetries affect various aspects of heat and particle transport in systems of the general type described above and obtain in the infinite volume limit the deviation from the theory in \cite{eckmann-young} to first-order. We verify our assumptions with extensive numerical simulations.