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  • Open Access

Contextuality in Anomalous Heat Flow

Naim E. Comar1,2,*, Danilo Cius1,†, Luis F. Santos1,‡, Rafael Wagner3,4,5,6,§, and Bárbara Amaral1,‖

  • *Contact author: naim.comar@usp.br
  • †Contact author: cius@if.usp.br
  • ‡Contact author: luisf@usp.br
  • §Contact author: rafael.wagner@inl.int
  • ‖Contact author: bamaral@if.usp.br
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PRX Quantum 6, 030359 – Published 22 September, 2025

DOI: https://doi.org/10.1103/f68k-cjx4

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 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 does 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 (0,τc) for a given critical time τc, 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 τc 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.

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Popular Summary

We are accustomed to observing a normal heat flow in our daily lives: when two bodies are in thermal contact, the hotter one warms the colder one. However, this heat flow can be inverted in quantum systems, a phenomenon known as anomalous heat flow. This occurs because quantum systems can share information in a particular way, using this information to exchange energy rather than performing work, as classical systems do. This counterintuitive phenomenon has significant physical and philosophical implications, particularly in thermodynamics, where normal heat flow is associated with a well-defined direction of time. However, research has yet to definitively prove that such a phenomenon cannot be replicated in systems described by classical mechanics. Our work certifies that, for a specific class of physical systems, anomalous heat flow occurs exclusively in a quantum scenario. More specifically, we demonstrate that these systems must exhibit a special characteristic called “contextuality,” which does not exist in classical systems.

Contextuality is the impossibility of making models about an underlying reality to describe a phenomenon without supposing that such reality is highly dependent on the experiment choice in which the phenomenon happens. Building on the concept of contextuality, we have achieved our results by extending a previously established method for certifying contextuality through the analysis of the average evolution of observable quantities, such as energy. The core of our generalization lies in considering a composition of distinct evolutions applied simultaneously to a single system. This approach allows us to account for a wide range of physical systems and interactions by simply varying the definition of “evolution.” This significantly enhances the applicability of the method for studying contextuality in physical systems, including quantum thermal machines.

Additionally, we anticipate that our work will open up new avenues for exploring nonclassical phenomena in thermodynamics, extending beyond just anomalous heat flow.

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PRX Quantum 6, 030359– Published 22 September, 2025
  • Received 20 August 2024
  • Revised 13 March 2025
  • Accepted 19 August 2025
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