Thermodynamic value of CHSH-induced side-information channels in a Szilard engine

• URL: http://arxiv.org/abs/2605.12044v1
• Date: Tue, 12 May 2026 12:25:37 GMT
• Title: Thermodynamic value of CHSH-induced side-information channels in a Szilard engine
• Abstract summary: We study the thermodynamic value of side-information channels induced by Bell-type correlations through a CHSH prediction task embedded into a Szilard-type feedback engine.<n>We show that the maximal average feedback work satisfies $langle W_maxrangle le k_B T ln 2, I(X:G)$, with equality achievable in the ideal quasistatic limit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study the thermodynamic value of side-information channels induced by Bell-type correlations through a CHSH prediction task embedded into a Szilard-type feedback engine. A thermal two-level system supplies a uniformly random physical microstate $X$, and a trusted referee encoding together with a nonsignalling correlation resource induces a controller bit $G$ that acts as side information about $X$. We show that the maximal average feedback work satisfies $\langle W_{\max}\rangle \le k_B T \ln 2 , I(X:G)$, with equality achievable in the ideal quasistatic limit. For the CHSH embedding considered here, the induced channel $X \to G$ is binary symmetric with success probability $p_{\rm win}=1/2+S(P)/8$, where $S(P)$ is the CHSH value. The corresponding reversible feedback work is $k_B T \ln 2 ,[1-h_2(p_{\rm win})]$, yielding a strict ordering of the optimal classical, quantum, and nonsignalling cases. The result should be interpreted as a thermodynamic valuation of CHSH-induced side information available to the controller, not as evidence that Bell nonlocality itself is a source of free energy. The analysis assumes that the controller receives only the compressed bit $G$ and does not include the thermodynamic cost of implementing the referee, the correlation resource, or the auxiliary preprocessing. A full-cycle analysis including controller-memory reset gives non-positive net work, consistent with the second law.

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