On apparent breaking the second law of thermodynamics in quantum transport studies

TL;DR

This paper investigates a quantum transport model where a recent theory predicts a persistent current that seemingly violates the second law of thermodynamics, but the authors find it results from approximation errors.

Contribution

The paper critically examines a recent theory predicting perpetual currents in quantum transport, clarifying the origin of the phenomenon and its relation to approximation errors.

Findings

The predicted permanent current is within the error margin of the asymptotic expansion.

Direct transport calculations show zero current, contradicting the recent theory.

The apparent violation is due to cancelling terms in the approximation, not a true physical violation.

Abstract

We consider a model for stationary electronic transport through a one-dimensional chain of two leads attached to a perturbed central region (quantum dot) in the regime where the theory proposed recently by Capek for a similar model of phonon transport predicts the striking phenomenon of a permanent current between the leads. This result based on a rigorous but asymptotic Davies theory is at variance with the zero current yielded by direct transport calculations which can be carried out in the present model. We find the permanent current to be within the error of the asymptotic expansion for finite couplings, and identify cancelling terms of the same order.