Thermo-mechanical transport in rotor chains

TL;DR

This paper derives and analyzes macroscopic diffusive equations for temperature and angular momentum in rotor chains under boundary forcing, revealing conditions for uphill energy diffusion and negative conductivity.

Contribution

It provides a formal derivation of stationary macroscopic equations from microscopic dynamics and explores their properties, including uphill diffusion and negative conductivity regimes.

Findings

Identification of parameter regimes with uphill energy diffusion

Discovery of regions with negative energy conductivity

Validation of macroscopic equations against microscopic simulations

Abstract

We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial differential equations with boundary conditions determined by the thermo-mechanical forcing. Instead of expensive Monte Carlo simulations of the underlying microscopic dynamics, we perform extensive numerical computations based on a finite difference method for the system of partial differential equations describing the macroscopic steady state. We first present a formal derivation of these stationary equations based on a linear response argument and local equilibrium assumptions. We then study various properties of the solutions to these equations. This allows to characterize the regime of parameters leading to uphill energy diffusion -- a situation in which the energy flows in the direction of the gradient of temperature -- and to identify regions of parameters corresponding to a negative energy conductivity (i.e. a positive linear response of the energy current to a gradient of temperature). The macroscopic equations we derive are consistent with some previous results obtained by numerical simulation of the microscopic physical system, which confirms their validity.