XOR-game winning probabilities fix the mutual information and thus the reversible Szilard work extractable from game-induced side information, yielding local, quantum and nonsignalling thermodynamic ceilings.
Thus the general binary-predicate construction reduces exactly to r=X⊕f(u, v), G=a⊕b⊕r, and the success probability is the XOR-game value p=ω G(P)
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Thermodynamic Value of XOR-Game-Induced Side Information in a Szilard Engine
XOR-game winning probabilities fix the mutual information and thus the reversible Szilard work extractable from game-induced side information, yielding local, quantum and nonsignalling thermodynamic ceilings.