Battery-Explicit Thermodynamic Witnesses of Bell Post-Quantumness

TL;DR

This paper introduces a thermodynamic witness for post-quantum Bell correlations using an explicit battery model, linking game success probabilities to energy transfer limits.

Contribution

It presents a novel battery-explicit thermodynamic framework that connects Bell game success probabilities with energy transfer bounds, distinguishing quantum from post-quantum correlations.

Findings

Mean battery charge equals game success probability times battery gap.

Tsirelson's bound acts as a quantum ceiling on battery charge.

PR-box behavior reaches the maximum single-excitation cap.

Abstract

We introduce a battery-explicit thermodynamic witness of post-quantum Bell correlations. In each round, a single supplied excitation is routed into an explicit two-level battery if and only if a Bell-game condition is satisfied. The routing operation is implemented by an energy-preserving controlled SWAP, with all logical control registers taken to be degenerate. Thus the correlation resource does not create energy; it only determines the probability that the supplied excitation reaches the battery. The construction is first formulated for finite two-player XOR games. For any such game, the mean battery charge is exactly the game success probability multiplied by the battery gap. Optimizing over local, quantum, or nonsignalling behaviours therefore turns the corresponding game values into local, quantum, or nonsignalling thermodynamic ceilings. For the CHSH game, Tsirelson's bound becomes a strict quantum ceiling on the mean battery charge, while a PR-box behaviour reaches the single-excitation cap. The witness is trusted-module rather than device-independent: it assumes calibrated Hamiltonians, correct classical wiring, and a trusted energy-preserving battery module. We also discuss a reversible-controller implementation, finite-statistics certification from work data, robustness to imperfect battery readout, and cyclic bookkeeping showing that no positive net work is obtained once fuel restoration and memory erasure are included.