Second law of the information thermodynamics with entanglement transfer

TL;DR

This paper introduces a new thermodynamic inequality incorporating entanglement transfer, showing that entanglement enhances work extraction beyond traditional limits during measurement and feedback processes.

Contribution

It presents a novel inequality linking Helmholtz free energy, entanglement of formation, and work, providing a clearer physical interpretation of entanglement's role in thermodynamics.

Findings

The new inequality is easier to achieve than previous bounds.

Entanglement transfer increases the maximum extractable work.

The work bound is extended by the amount of entanglement extracted.

Abstract

We present a new inequality which holds in the thermodynamical processes with measurement and feedback controls with using only the Helmholtz free energy and the entanglement of formation: $W_{\mathrm{ext}}\le-\Delta F-k_{B}T\Delta E_{F}$. The quantity $-\Delta E_{F}$, which is positive, expresses the amount of entanglement transfer from the system $S$ to the probe $P$ through the interaction $\hat{U}_{SP}$ during the measurement. It is easier to achieve the upper bound in the new inequality than in the Sagawa-Ueda inequality [Phys. Rev. Lett. 100 080403 (2008)]. The new inequality has clear physical meaning: in the above thermodynamical processes, the work which we can extract from the thermodynamic system is greater than the upper bound in the conventional thermodynamics by the amount of the entanglement extracted by the measurement.