Nonequilibrium density matrix for simultaneous heat and charge steady-state transport in quantum open systems

TL;DR

This paper generalizes the nonequilibrium density matrix for quantum systems with simultaneous heat and charge transport, linking it to entropy production and fluxes, and provides an explicit example with non-interacting fermions.

Contribution

It extends Hershfield's method to systems with both heat and charge currents, deriving a generalized Gibbs-like ensemble consistent with McLennan-Zubarev theory.

Findings

The NE density matrix incorporates entropy production terms.

The generalized ensemble accurately describes steady-state heat and charge transport.

Explicit example demonstrates the approach for non-interacting fermions.

Abstract

We suggest a generalisation of the expression of the nonequilibrium density matrix obtained by Hershfield's method for the cases where both heat and charge steady state currents are present in a quantum open system. The finite-size quantum system, connected to two temperature and particle reservoirs, is driven out of equilibrium by the presence of both a temperature gradient and a chemical potential gradient between the two reservoirs. We show that the NE density matrix is given by a generalised Gibbs-like ensemble, and is in full agreement with the general results of the McLennan-Zubarev nonequilibrium ensembles. The extra non-equilibrium terms are related to the entropy production in the system and characterise the fluxes of heat and particle.An explicit example, for the lowest order expansion, is provide for a model system of non-interacting fermions.