Energy of the symmetrization entanglement

TL;DR

This paper investigates the energy associated with symmetrization entanglement in a Bose-Einstein condensate, revealing that the work extractable equals the total thermodynamic energy of the condensate, with implications for quantum and fundamental physics.

Contribution

It introduces a novel analysis of symmetrization entanglement energy in condensates, linking measurement-induced work to thermodynamic energy and exploring broader implications.

Findings

Work extracted equals the total thermodynamic energy of the condensate.

Measurement of a boson state under certain conditions yields complete energy extraction.

Results suggest fundamental implications for pair creation in QED vacuum.

Abstract

When a measurement is carried out on one of the entangled parties, the second party can extract work owing to the reduction in its entropy. Here we inquire the amount of work/energy corresponding to the symmetrization entanglement of identical particles (bosons) in a condensate. One measures the quantum state of a particular boson which can be performed only under some certain conditions. We learn that the extracted work comes out to be the \textit{complete} thermodynamical energy present in the condensate. %We learn that the work extracted by the remaining part of the condensate is equal to the excitation energy of the measured boson times the thermodynamical probability of being in the excited state, i.e., $\hbar \omega_{eg} \times \exp(-\hbar \omega_{eg}/k_BT)$. We study the phenomenon in an interacting Bose-Einstein condensate. Then, we discuss that the results may also have fundamental implications on the pair creation in QED vacuum.