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arXiv:2609.37592

Quantum Statistical Thermal Engine at the BCS-BEC crossover

Santiago Henríquez Lira, Felipe Isaule, Martín HvE Groves, Francisco J. Peña, Patricio Vargas, Thomás Fogarty

cond-mat.stat-mechcond-mat.quant-gasquant-phSubmitted Sep 29, 2026• Announced Sep 30, 2026• 0 citations• Revised Oct 1, 2026 (v2)
v1 · Sep 29, 2026v2 · Oct 1, 2026
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Abstract

We propose a quantum heat engine based on a two-component Fermi gas with s-wave contact interaction, operating across the BCS-BEC crossover. The work is extracted from the statistical properties of the gas, which are controlled by the interaction, rather than relying solely on compression and expansion stages. Using the functional renormalization group formalism, we obtain the equation of state in a non-perturbative form along the crossover, encompassing the superfluid-normal phase transition. The cycle combines isentropic density strokes, isochoric thermalization, and isothermal interaction sweeps. This construction makes it possible to integrate features of both Otto and Carnot cycles, in which the system simultaneously saturates both efficiency limits without the net work vanishing. In the absence of density variations, the cycle reduces to a statistical Stirling-like engine, in which the work generated arises exclusively from the interaction, achieving efficiencies up to $38\%$. A pronounced asymmetry emerges through the crossover, giving rise to distinct operating regimes depending on the trajectory followed in the phase diagram. Consequently, the same architecture can be tuned to function as an engine, refrigerator, accelerator, or heater. These findings highlight pairing correlations as a versatile thermodynamic resource for quantum heat machines.

Comments
14 pages, 10 figures

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We propose a quantum heat engine based on a two-component Fermi gas with s-wave contact interaction, operating across the BCS-BEC crossover. The work is extracted from the statistical properties of the gas, which are controlled by the interaction, rather than relying solely on compression and expansion stages. Using the functional renormalization group formalism, we obtain the equation of state in a non-perturbative form along the crossover, encompassing the superfluid-normal phase transition. The cycle combines isentropic density strokes, isochoric thermalization, and isothermal interaction sweeps. This construction makes it possible to integrate features of both Otto and Carnot cycles, in which the system simultaneously saturates both efficiency limits without the net work vanishing. In the absence of density variations, the cycle reduces to a statistical Stirling-like engine, in which the work generated arises exclusively from the interaction, achieving efficiencies up to 38%38\%38%. A pronounced asymmetry emerges through the crossover, giving rise to distinct operating regimes depending on the trajectory followed in the phase diagram. Consequently, the same architecture can be tuned to function as an engine, refrigerator, accelerator, or heater. These findings highlight pairing correlations as a versatile thermodynamic resource for quantum heat machines.
Abstract A key focus of designing quantum thermal devices is the potential advantage that can be gleaned from genuine quantum effects when compared to classical devices. The recent experimental realization of the Pauli engine (Koch et al 2023 Nature 621 723)—where energy is extracted via changes in particle statistics as an alternative to conventional heat sources—has opened new avenues of research where quantum statistics can be considered as a thermodynamic resource. In this work we propose hybrid quantum heat engines which can utilize additional strokes that change the single particle statistics between bosonic and fermionic descriptions during the cycle. To accomplish this we consider the 1D Lieb–Liniger gas, in which the s-wave interactions can be tuned between the non-interacting and the hard-core limit, which are described by bosonic and fermionic statistics respectively. We show that by suitably choosing where to implement these statistical strokes during an Otto-like cycle in the quasi-static limit, the efficiency and work output can be significantly enhanced when compared to fully bosonic or fully fermionic engines. Furthermore, in the degenerate regime our engine can operate at the Carnot efficiency, due to the interplay between the different contributions of heat and work induced by the statistical strokes. Finally, we highlight how our thermodynamic cycles can realize other thermal operations, such as refrigerators, promising similar statistical enhancements for a wide range of temperatures.
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We investigate a quantum thermal machine composed of two qubits coupled through a Raman-induced exchange interaction and driven by inhomogeneous transition frequencies. The system is analyzed within Carnot, Otto, and Stirling thermodynamic cycles, including the Stirling cycle with and without regeneration. We identify the conditions under which the device operates as a heat engine, refrigerator, thermal accelerator, or heater. Efficiency maps and operational-mode diagrams reveal well-defined boundaries in parameter space, governed by the frequency ratio r=ωˉ/ωr=\barω/ωr=ωˉ/ω, the coupling strength ggg, and the thermal gradient between reservoirs. The Carnot cycle exhibits sharp transitions between engine and refrigerator regimes, while the Otto cycle displays a richer structure with the coexistence of all operational modes. The Stirling cycle shows enhanced versatility and performance, particularly when assisted by a regenerator, where near-ideal efficiencies are achieved. Overall, the Raman-type interaction introduces a controllable left-right asymmetry that enables nontrivial manipulation of thermodynamic behavior through frequency tuning.
Abstract We study the thermodynamic performance of a finite-time non-regenerative quantum Stirling-like cycle used as a heat engine. We consider specifically the case in which the working substance (WS) is a two-level system (TLS). The Stirling cycle is made of two isochoric transformations separated by a compression and an expansion stroke during which the WS is in contact with a thermal reservoir. To describe these two strokes we derive a non-Markovian master equation which allows to study the real-time dynamics of a driven open quantum system with arbitrary fast driving. Following the real-time dynamics of the WS using this master equation, the endpoints of the isotherms can deviate from the equilibrium thermal states. The role of this deviation in the performance of the heat engine is addressed. We found that the finite-time dynamics and thermodynamics of the cycle depend non-trivially on the different time scales at play. In particular, driving the WS at a time scale comparable to the resonance time of the bath enhances the performance of the cycle and allows for an efficiency higher than the efficiency of the quasistatic cycle, but still below the Carnot bound. However, by adding thermalization of the WS with the baths at the end of compression/expansion processes one recovers the conventional scenario in which efficiency decreases by speeding up the processes. In addition, the performance of the cycle is dependent on the compression/expansion speeds asymmetrically, which suggests new freedom in optimizing quantum heat engines. The maximum output power and the maximum efficiency are obtained almost simultaneously when the real-time endpoints of the compression/expansion processes are considered instead of the equilibrium thermal endpoint states. However, the net extractable work always declines by speeding up the drive.
In this article, we show that a quantum gas, a collection of massive, non-interacting, indistinguishable quantum particles, can be realized as a thermodynamic machine as an artifact of energy quantization and, hence, bears no classical analog. Such a thermodynamic machine depends on the statistics of the particles, the chemical potential, and the spatial dimension of the system. Our detailed analysis demonstrates the fundamental features of quantum Stirling cycles, from the viewpoint of particle statistics and system dimensions, that helps us to realize desired quantum heat engines and refrigerators by exploiting the role of quantum statistical mechanics. In particular, a clear distinction between the behavior of a Fermi gas and a Bose gas is observed in one dimension, rather than in higher dimensions, solely due to the innate differences in their particle statistics indicating the conspicuous role of a quantum thermodynamic signature in lower dimensions.
Particle-particle correlations, characterized by Glauber’s second-order correlation function, play an important role in the understanding of various phenomena in radio and optical astronomy, quantum and atom optics, particle physics, condensed matter physics, and quantum many-body theory. However, the relevance of such correlations to quantum thermodynamics has so far remained illusive. Here, we propose and investigate a class of quantum many-body thermal machines whose operation is directly enabled by second-order atom-atom correlations in an ultracold atomic gas. More specifically, we study quantum thermal machines that operate in a sudden interaction-quench Otto cycle and utilize a one-dimensional Lieb-Liniger gas of repulsively interacting bosons as the working fluid. The atom-atom correlations in such a gas are different to those of a classical ideal gas, and are a result of the interplay between interparticle interactions, quantum statistics, and thermal fluctuations. We show that operating these thermal machines in the intended regimes, such as a heat engine, refrigerator, thermal accelerator, or heater, would be impossible without such atom-atom correlations. Our results constitute a step forward in the design of conceptually new quantum thermodynamic devices which take advantage of uniquely quantum resources such as quantum coherence, correlations, and entanglement.