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We demonstrate that both Wigner's form of Bell's inequalities as well as aform of the second law of thermodynamics, as manifest in Carath\'{e}odory'sprinciple, can be derived from the same simple experimental and statisticalmechanical assumptions combined with the trivial behavior of integers. Thissuggests that Bell's theorem is merely a well-disguised statement of the secondlaw. It also suggests that entanglement is necessary for quantum theory to bein 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 necessaryfor consistency with the third law.

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