Mean battery charge equals Bell game success probability times battery gap, turning local, quantum, and nonsignaling game values into thermodynamic ceilings for XOR games.
Then the winning condition is satisfied with probability one
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Battery-Explicit Thermodynamic Witnesses of Bell Post-Quantumness
Mean battery charge equals Bell game success probability times battery gap, turning local, quantum, and nonsignaling game values into thermodynamic ceilings for XOR games.