A rigorous scattering approach to quasifree fermionic systems out of equilibrium

TL;DR

This paper rigorously constructs and analyzes the nonequilibrium steady state of a quasifree fermionic system, demonstrating positive entropy production using scattering theory within an axiomatic quantum framework.

Contribution

It introduces a rigorous scattering approach to describe nonequilibrium steady states in quasifree fermionic systems, specifically the XY chain with reservoirs.

Findings

Proves the existence of nonequilibrium steady states.

Shows the entropy production rate is strictly positive.

Employs time-dependent and stationary scattering theory rigorously.

Abstract

Within the rigorous axiomatic framework for the description of quantum mechanical systems with a large number of degrees of freedom, we construct the so-called nonequilibrium steady state for the quasifree fermionic system corresponding to the isotropic XY chain in which a finite sample, subject to a local gauge breaking anisotropy perturbation, is coupled to two thermal reservoirs at different temperatures. Using time dependent and stationary scattering theory, we rigorously prove, from first principles, that the nonequilibrium system under consideration is thermodynamically nontrivial, i.e., that its entropy production rate is strictly positive.