A Chain, a Bath, a Sink, and a Wall

Stefano Iubini,Stefano Lepri,Antonio Politi,Roberto Livi,Gian-Luca Oppo

doi:10.3390/e19090445

Abstract

We numerically investigate out-of-equilibrium stationary processes emerging in a Discrete Nonlinear Schrödinger chain in contact with a heat reservoir (a bath) at temperature T L and a pure dissipator (a sink) acting on opposite edges. Long-time molecular-dynamics simulations are performed by evolving the equations of motion within a symplectic integration scheme. Mass and energy are steadily transported through the chain from the heat bath to the sink. We observe two different regimes. For small heat-bath temperatures T L and chemical-potentials, temperature profiles across the chain display a non-monotonous shape, remain remarkably smooth and even enter the region of negative absolute temperatures. For larger temperatures T L , the transport of energy is strongly inhibited by the spontaneous emergence of discrete breathers, which act as a thermal wall. A strongly intermittent energy flux is also observed, due to the irregular birth and death of breathers. The corresponding statistics exhibit the typical signature of rare events of processes with large deviations. In particular, the breather lifetime is found to be ruled by a stretched-exponential law.

Highlights

The study of nonequilibrium thermodynamics of systems composed of a relatively small number of particles is motivated by the need for a deeper theoretical understanding of the statistical laws leading to the possibility of manipulating small-scale systems like biomolecules, colloids, or nano-devices
We have investigated the behavior of a discrete nonlinear Schrödinger equation sandwiched between a heat reservoir and a mass/energy dissipator
Two different regimes have been identified upon changing the temperature TL of the heat reservoir, while keeping fixed the properties of the dissipator

Summary

Introduction

The study of nonequilibrium thermodynamics of systems composed of a relatively small number of particles is motivated by the need for a deeper theoretical understanding of the statistical laws leading to the possibility of manipulating small-scale systems like biomolecules, colloids, or nano-devices. Instead, the chain is put in contact with thermal baths at its edges, non-equilibrium stationary states characterized by a gradient of temperature and chemical potential emerge [13]. Local equilibrium is typically satisfied so that the overall state of the chain can be conveniently represented as a path in the ( a, h) plane connecting two points corresponding to the thermodynamic variables imposed by the two reservoirs. Extends up to the dissipator edge and it progressively shrinks in favour of a positive-temperature region (on the other side of the chain) In this regime, the dynamics are controlled by the spontaneous formation (birth) and disappearance (death) of discrete breathers.

Model and Methods

Low-Temperature Regime

High Temperature Regime

Statistical Analysis

Conclusions