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arXiv:2603.17078 · Physical review. E

Quantifying entanglement in quantum thermodynamics via separability constraints

Joan Alba, Laura Ares, Jan Sperling, Julien Pinske

quant-phSubmitted Mar 17, 2026• Announced Mar 19, 2026• 0 citations
v1 · Mar 17, 2026v2 · Mar 20, 2026v3 · Oct 26, 2026
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Abstract

The role of quantum entanglement in thermodynamical systems remains elusive. Does entanglement result in thermodynamic advantages or does it impose fundamental limitations? Here, we unambiguously quantify the amount of heat and work in a quantum system that is due to the presence of entanglement. This is achieved by constraining the system's non-equilibrium dynamics to separable states, thereby isolating the impact entanglement has on thermodynamic effects. Unlike thermodynamic entanglement measures, which signify a loose connection between entanglement and thermodynamic properties, imposing a constraint constitutes an active intervention into a system -- answering how much of a system's thermodynamics is caused by (not correlated with) its quantumness. We benchmark our theory by applying the constrained dynamics to several multipartite systems, including quantum batteries and quantum refrigerators.

Journal reference
Phys. Rev. E 114, 024157 (2026)
DOI
10.1103/sjqy-gnvp
Comments
14 pages, 6 figures

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The role of quantum entanglement in thermodynamical systems remains elusive. Does entanglement result in thermodynamic advantages or does it impose fundamental limitations? Here, we unambiguously quantify the amount of heat and work in a quantum system that is due to the presence of entanglement. This is achieved by constraining the system's non-equilibrium dynamics to separable states, thereby isolating the impact entanglement has on thermodynamic effects. Unlike thermodynamic entanglement measures, which signify a loose connection between entanglement and thermodynamic properties, imposing a constraint constitutes an active intervention into a system -- answering how much of a system's thermodynamics is caused by (not correlated with) its quantumness. We benchmark our theory by applying the constrained dynamics to several multipartite systems, including quantum batteries and quantum refrigerators.
Understanding the thermodynamics of quantum systems is of fundamental importance, from both theoretical and experimental perspectives. A growing interest has been recently given to small self-contained quantum thermal machines, the functioning of which requires no external source of work or control, but only incoherent interactions with thermal baths. The simplicity of such machines makes them and ideal test-bed for exploring quantum thermodynamics. So far, however, the importance of quantum effects in these machines has remained elusive. Here we show that entanglement, the paradigmatical quantum effect, plays a fundamental role in small self-contained quantum refrigerators, as it can enhance cooling and energy transport -- except notably when the efficiency is close to the Carnot limit. Hence a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling. More generally, our work shows that entanglement opens new possibilities in thermodynamics.
We demonstrate that the presence of entanglement in macroscopic bodies (e.g., solids) in thermodynamical equilibrium could be revealed by measuring heat capacity. The idea is that if the system was in a separable state, then for certain Hamiltonians heat capacity would not tend asymptotically to zero as the temperature approaches absolute zero. Since this would contradict the third law of thermodynamics, one concludes that the system must contain entanglement. The separable bounds are obtained by minimalization of the heat capacity over separable states and using its universal low-temperature behavior. Our results open up a possibility to use standard experimental techniques of solid-state physics---namely, heat-capacity measurements---to detect entanglement in macroscopic samples.
How much work can be extracted from a heat bath using a thermal machine operating at the quantum level? In this work, we establish a framework of work extraction in the presence of quantum correlations as they naturally emerge in quantum thermodynamics beyond the weak-coupling regime. Quantum correlations and entanglement, as they are ubiquitously encountered when putting systems into contact with a bath, emerge as a limitation to work extraction, rather than as an advantage. We bring together concepts of quantum thermodynamics with those of non-equilibrium dynamics, in a rigorous but physically motivated approach. We discuss various limits that relate to known results and put our work into context of approaches to finite-time quantum thermodynamics.
The heat capacity of a system quantifies how it energetically responds to changes in temperature at equilibrium. Whilst this quantity is positive and even additive for non-interacting systems, self-gravitating systems such as stars or subsystems of strongly interacting quantum systems are known to have negative or anomalous specific heat capacities. In this work, we investigate how the presence of entanglement at equilibrium can influence how an interacting system responds energetically to changes in temperature. We examine the local heat capacity of interacting quantum systems providing an analytical understanding for when anomalies occur. Most interestingly, we find a connection between local heat capacity anomalies and entanglement by deriving a separability bound based on the fluctuations of local and interaction energies. We illustrate our results with two examples (i) a nearest neighbour spin-1/2 chain and (ii) two coupled quantum harmonic oscillators. Lastly, we provide an information-theoretic formula connecting mutual information and athermality to the non-additivity of the heat capacity. Our results provide model-independent thermodynamic entanglement detection bounds and insight into the relationship between quantum correlations and the heat capacity of quantum systems.
Abstract A thermodynamic theory of quantum entanglement as well as the establishment of rigorous formal connections between the laws of thermodynamics and the phenomenology of entanglement are currently open areas of investigation. In this quest, a core problem is embodied by the understanding of the role that entanglement plays in processes of work extraction. Here, by considering information thermodynamics-based protocols, we answer the question “Is it possible to infer, quantitatively, quantum correlations by considering work-extraction schemes?”. Our experimental settings consist of suitably designed multi-photon optical interferometers able to address the case of both bipartite and multipartite entangled states. We compare the performance of such criteria to that of witnesses of entanglement based on the violation of Bell-like tests, showing their inherently different nature. Our work contributes strongly to the ongoing efforts in establishing photonic systems as a platform for experiments in information thermodynamics.
Quantum entanglement can cause the efficiency of a heat engine to be greater than the efficiency of the Carnot cycle. However, this does not mean a violation of the second law of thermodynamics, since there is no local equilibrium for pure quantum states, and, in the absence of local equilibrium, thermodynamics cannot be formulated correctly. Von Neumann entropy is not a thermodynamic quantity, although it can characterize the ordering of a system. In the case of the entanglement of the particles of the system with the environment, the concept of an isolated system should be refined. In any case, quantum correlations cannot lead to a violation of the second law of thermodynamics in any of its formulations. This article is devoted to a technical discussion of the expected results on the role of quantum entanglement in thermodynamics.