Contextuality in Anomalous Heat Flow

In classical thermodynamics, heat must spontaneously flow from hot to cold systems. In quantum thermodynamics, the same law applies when considering multipartite product thermal states evolving unitarily. If initial correlations are present, anomalous heat flow can happen, temporarily making cold thermal states colder and hot thermal states hotter. Such an effect can happen due to entanglement but also because of classical randomness, hence lacking a direct connection with nonclassicality. In this work, we introduce scenarios in which anomalous heat flow have a direct link to nonclassicality, defined as the failure of noncontextual models to explain experimental data. We start by extending known noncontextuality inequalities to a setup in which sequential transformations are considered. We then show a class of quantum prepare-transform-measure protocols, characterized by a time interval <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">(</a:mo><a:mn>0</a:mn><a:mo>,</a:mo><a:msub><a:mi>τ</a:mi><a:mi>c</a:mi></a:msub><a:mo stretchy="false">)</a:mo></a:math> for a given critical time <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>τ</e:mi><e:mi>c</e:mi></e:msub></e:math>, where anomalous heat flow happens only if a noncontextuality inequality is violated. We also analyze a recent experiment from and find the critical time <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>τ</g:mi><g:mi>c</g:mi></g:msub></g:math> based on the authors’ experimental parameters. We conclude by investigating heat flow in the evolution of two-qudit systems, showing that our findings are not an artifact of using two-qubit systems.