Cold spots in quantum systems far from equilibrium: local entropies and temperatures near absolute zero

TL;DR

This paper investigates the possibility of achieving local temperatures near absolute zero in nonequilibrium quantum systems, demonstrating that destructive quantum interference can facilitate such low temperatures and introducing a local entropy measure.

Contribution

It introduces a method to compute local temperatures near absolute zero in nonequilibrium quantum conductors and defines a local entropy metric consistent with the third law.

Findings

Local temperatures close to absolute zero are achievable via destructive quantum interference.

The local entropy tends to zero as the probe temperature approaches zero.

Excellent agreement between numerical and analytic results using the Sommerfeld expansion.

Abstract

We consider a question motivated by the third law of thermodynamics: can there be a local temperature arbitrarily close to absolute zero in a nonequilibrium quantum system? We consider nanoscale quantum conductors with the source reservoir held at finite temperature and the drain held at or near absolute zero, a problem outside the scope of linear response theory. We obtain local temperatures close to absolute zero when electrons originating from the finite temperature reservoir undergo destructive quantum interference. The local temperature is computed by numerically solving a nonlinear system of equations describing equilibration of a scanning thermoelectric probe with the system, and we obtain excellent agreement with analytic results derived using the Sommerfeld expansion. A local entropy for a nonequilibrium quantum system is introduced, and used as a metric quantifying the departure from local equilibrium. It is shown that the local entropy of the system tends to zero when the probe temperature tends to zero, consistent with the third law of thermodynamics.