On the asymptotic scaling of the von Neumann entropy in quasifree fermionic right mover/left mover systems

TL;DR

This paper investigates the asymptotic behavior of von Neumann entropy in quasifree fermionic right mover/left mover systems, revealing its nonvanishing nature and relation to thermal states, with criteria for entropy density to vanish.

Contribution

It provides a detailed analysis of the entropy scaling in quasifree fermionic systems, including conditions for entropy density to vanish, covering various states like nonequilibrium steady states and thermal equilibrium.

Findings

Entropy density is generally nonvanishing for large subsystems.

The formalism applies to nonequilibrium steady states, thermal states, and ground states.

A criterion for the vanishing of entropy density for general Fermi functions.

Abstract

For the general class of quasifree fermionic right mover/left mover systems over the infinitely extended two-sided discrete line introduced in [8] within the algebraic framework of quantum statistical mechanics, we study the von Neumann entropy of a contiguous subsystem of finite length in interaction with its environment. In particular, under the assumption of spatial translation invariance, we analyze the asymptotic behavior of the von Neumann entropy for large subsystem lengths and prove that its leading order density is, in general, nonvanishing and displays the signature of a mixture of the independent thermal species underlying the right mover/left mover system. As special cases, the formalism covers so-called nonequilibrium steady states, thermal equilibrium states, and ground states. Moreover, for general Fermi functions, we derive a necessary and sufficient criterion for the von Neumann entropy density to vanish.