Thermodynamic precision in the nonequilibrium exchange scenario

TL;DR

This paper investigates thermodynamic uncertainty relations in a two-qubit entangled nonequilibrium steady state, exploring how entanglement influences work precision and the validity of these relations under different unitaries.

Contribution

It analytically demonstrates the conditions under which thermodynamic uncertainty relations hold or break down in entangled steady states, highlighting entanglement's role in work absorption.

Findings

Thermodynamic uncertainty relations can be constructed for certain unitaries.

These relations may not hold universally for all unitaries.

Entanglement can reduce uncertainty in work absorption, as shown by state projections.

Abstract

We discuss exchange scenario's thermodynamic uncertainty relations for the work done on a two-qubit entangled nonequilibrium steady state obtained by coupling the two qubits and putting each of them in weak contact with a thermal bath. In this way we investigate the use of entangled nonequilibrium steady states as end-points of thermodynamic cycles. In this framework, we prove analytically that for a paradigmatic unitary it is possible to construct an exchange scenario's thermodynamic uncertainty relation. However, despite holding in many cases, we also show that such relation ceases to be valid when considering other suitable unitary quenches. Furthermore, this paradigmatic example allows us to shed light on the role of the entanglement between the two qubits for precise work absorption. By considering the projection of the entangled steady state onto the set of separable states, we provide examples where such projection implies an increase of the relative uncertainty, showing the usefulness of entanglement.