The necessity of entanglement and the equivalency of Bell's theorem with the second law of thermodynamics

TL;DR

This paper argues that Bell's theorem is essentially equivalent to the second law of thermodynamics, implying that entanglement is necessary for quantum theory to align with thermodynamic principles.

Contribution

It demonstrates the derivation of Bell's inequalities and the second law from common assumptions, linking quantum entanglement to thermodynamic consistency.

Findings

Bell's theorem can be derived from thermodynamic principles.

Entanglement is necessary for quantum theory to comply with the second law.

Bell's inequalities are mathematically equivalent to a form of the second law.

Abstract

We demonstrate that both Wigner's form of Bell's inequalities as well as a form of the second law of thermodynamics, as manifest in Carath\'{e}odory's principle, can be derived from the same simple experimental and statistical mechanical assumptions combined with the trivial behavior of integers. This suggests that Bell's theorem is merely a well-disguised statement of the second law. It also suggests that entanglement is necessary for quantum theory to be in full accord with the second law and thus builds on the results of Wiesniak, Vedral, and Brukner \cite{Marcin-Wiesniak:2008fv} who showed it was necessary for consistency with the third law.