Contextuality in anomalous heat flow

TL;DR

This paper explores the connection between anomalous heat flow in quantum thermodynamics and quantum noncontextuality, demonstrating that certain heat flow phenomena are linked to violations of noncontextuality inequalities.

Contribution

It introduces a framework linking anomalous heat flow to nonclassicality via noncontextuality inequalities and analyzes experimental and theoretical scenarios.

Findings

Anomalous heat flow occurs only when noncontextuality inequalities are violated.

Extended noncontextuality inequalities are applicable to sequential transformations.

Experimental parameters from Micadei et al. are used to identify critical time for anomalous heat flow.

Abstract

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 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 where anomalous heat flow \emph{does} have a direct link to nonclassicality, defined to be the failure of noncontextual models to explain experimental data. We start by extending known noncontextuality inequalities to a setup where sequential transformations are considered. We then show a class of quantum prepare-transform-measure protocols, characterized by time intervals $(0,\tau_c)$ for a given critical time $\tau_c$, where anomalous heat flow happens only if a noncontextuality inequality is violated. We also analyze a recent experiment from Micadei et. al. [Nat. Commun. 10, 2456 (2019)] and find the critical time $\tau_c$ based on their experimental parameters. We conclude by investigating heat flow in the evolution of two qutrit systems, showing that our findings are not an artifact of using two-qubit systems.