bibkey: micadei2019correlations
authors: Kaonan Micadei, John P. S. Peterson, Alexandre M. Souza, Roberto S. Sarthour, Ivan S. Oliveira, Gabriel T. Landi, Tiago B. Batalhão, Roberto M. Serra, Eric Lutz
year: 2019
title: Reversing the direction of heat flow using quantum correlations
doi: null
url: https://doi.org/10.1038/s41467-019-10333-7
claim: Thermal marginal relative entropies equal beta times energy change minus entropy change; joint unitary entropy conservation identifies the sum of marginal entropy changes with the change of mutual information.
strata_touched:
  - D5/S3/Quantum/Information/CorrelatedGibbsEnergyIdentity
license: citation-only
triage: anchor

Energy and initial correlations

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DOI: 10.1038/s41467-019-10333-7

The canonical article locator is https://doi.org/10.1038/s41467-019-10333-7. Crossref metadata and the full Nature Communications article were opened. The title, author list, journal volume 10, article 2456, and year 2019 agree.

Methods, “Heat current between initially correlated systems,” equations (6) and (7), give D(rho_i’ || rho_i) = beta_i Delta E_i - Delta S_i for initially thermal marginals. The text immediately following equation (8) gives Delta S_A + Delta S_B = Delta I(A:B) for the isolated joint system. Their sum is the weighted energy identity, before the additional energy conservation substitution used in the paper’s heat-flow formula.

The Lean statement uses arbitrary finite nonempty subsystem index types, the existing normalized matrix exponential at -beta H, and a joint unitary. It retains the initial mutual information and imposes neither a product initial state nor energy conservation. It allows every real beta. The experiment concerns two spins; no experimental outcome, thermalization assertion, sign of heat flow, or equation (164.2) is certified here.