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

TL;DR

This paper quantifies the thermodynamic value of side-information channels created by Bell-type correlations in a Szilard engine, revealing how quantum and nonsignalling resources influence work extraction.

Contribution

It introduces a thermodynamic framework for CHSH-induced side information, comparing classical, quantum, and nonsignalling cases in a Szilard engine context.

Findings

Maximal average feedback work is bounded by $k_B T ext{ln} 2$ times mutual information.

The induced channel is binary symmetric with success probability related to the CHSH value.

Quantum and nonsignalling resources provide a strict ordering of work extraction capabilities.

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.