Negative-temperature Fourier transport in one-dimensional systems

TL;DR

This paper explores how one-dimensional diffusive systems can exhibit negative absolute temperatures and still follow a Fourier law, revealing novel transport regimes with potential implications for thermodynamics.

Contribution

It introduces models of negative-temperature transport in 1D systems and demonstrates the applicability of Fourier law in these unconventional regimes.

Findings

Negative temperatures can be realized in 1D diffusive systems.

Fourier law describes transport even with negative temperature profiles.

Negative-temperature transport occurs in both deterministic and stochastic models.

Abstract

We investigate nonequilibrium steady states in a class of one-dimensional diffusive systems that can attain negative absolute temperatures. The cases of a paramagnetic spin system, a Hamiltonian rotator chain and a one-dimensional discrete linear Schr\"odinger equation are considered. Suitable models of reservoirs are implemented to impose given, possibly negative, temperatures at the chain ends. We show that a phenomenological description in terms of a Fourier law can consistently describe unusual transport regimes where the temperature profiles are entirely or partially in the negative-temperature region. Negative-temperature Fourier transport is observed both for deterministic and stochastic dynamics and it can be generalized to coupled transport when two or more thermodynamic currents flow through the system.