An exactly solvable dissipative transport model

TL;DR

This paper introduces a one-dimensional lattice model for energy transport with dissipation, providing explicit solutions for stationary distributions and analyzing the effects of symmetric and asymmetric transport.

Contribution

It presents an exactly solvable dissipative transport model with explicit stationary distribution solutions, covering both symmetric and asymmetric cases.

Findings

Explicit stationary distribution derived

Conditions for distribution factorization identified

Model applicable to physically relevant dissipative systems

Abstract

We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, which allows us to study symmetric as well as asymmetric cases. We derive sufficient conditions for the factorization of the N-body stationary distribution and give an explicit solution for the latter, before briefly discussing physically relevant situations.