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arXiv:2606.19310

Exclusion Statistics as a Thermodynamic Resource in Quantum Heat Engines

Sampurna Karmakar, Aziz Hasan, Sourin Das

cond-mat.mes-hallquant-phSubmitted Jun 17, 2026• Announced Jun 18, 2026
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Abstract

The maximum power extractable from a quantum thermoelectric heat engine operating with free fermion carriers is bounded by the universal Whitney limit, $P_{\text{fermion}}^{\max} \simeq 0.0321π^2 k_B^2(T_L-T_R)^2/h$. We demonstrate that this bound is not fundamental to quantum heat engines but is instead an artifact of fermionic statistics. Within the nonlinear Landauer-Büttiker framework, a bosonic working medium yields a strictly enhanced universal maximum power, $P_{\text{boson}}^{\max} = (\ln 2)^2\, k_B^2(T_L-T_R)^2/h$, exceeding the fermionic limit by a factor of $(\ln 2)^2/(0.0321π^2) \approx 1.52$. We propose magnon transport through a ferromagnetic spin chain as an experimentally viable bosonic realization. Incorporating Haldane fractional exclusion statistics with parameter $g$ provides a continuous interpolation between the bosonic ($g = 0$) and fermionic ($g = 1$) limits, revealing a monotonic enhancement of maximum power for $g < 1$ at reduced bias cost. These results establish quantum statistical exclusion as a previously unrecognized and independently tunable thermodynamic resource, opening performance regimes inaccessible to conventional carrier-engineering approaches.

Comments
6 pages, 4 figures

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The maximum power extractable from a quantum thermoelectric heat engine operating with free fermion carriers is bounded by the universal Whitney limit, Pfermionmax⁡≃0.0321π2kB2(TL−TR)2/hP_{\text{fermion}}^{\max} \simeq 0.0321π^2 k_B^2(T_L-T_R)^2/hPfermionmax​≃0.0321π2kB2​(TL​−TR​)2/h. We demonstrate that this bound is not fundamental to quantum heat engines but is instead an artifact of fermionic statistics. Within the nonlinear Landauer-Büttiker framework, a bosonic working medium yields a strictly enhanced universal maximum power, Pbosonmax⁡=(ln⁡2)2 kB2(TL−TR)2/hP_{\text{boson}}^{\max} = (\ln 2)^2\, k_B^2(T_L-T_R)^2/hPbosonmax​=(ln2)2kB2​(TL​−TR​)2/h, exceeding the fermionic limit by a factor of (ln⁡2)2/(0.0321π2)≈1.52(\ln 2)^2/(0.0321π^2) \approx 1.52(ln2)2/(0.0321π2)≈1.52. We propose magnon transport through a ferromagnetic spin chain as an experimentally viable bosonic realization. Incorporating Haldane fractional exclusion statistics with parameter ggg provides a continuous interpolation between the bosonic (g=0g = 0g=0) and fermionic (g=1g = 1g=1) limits, revealing a monotonic enhancement of maximum power for g<1g < 1g<1 at reduced bias cost. These results establish quantum statistical exclusion as a previously unrecognized and independently tunable thermodynamic resource, opening performance regimes inaccessible to conventional carrier-engineering approaches.
By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Here, we examine using wave function symmetry as a resource to enhance the performance of a quantum Otto engine. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this work by incorporating a singular interaction that allows the effective symmetry to be tuned between the bosonic and fermionic limits. In this framework, the particles can be treated as anyons subject to Haldane’s generalized exclusion statistics. Solving the dynamics analytically using the framework of “statistical anyons”, we explore the interplay between interparticle interactions and wave function symmetry on engine performance.
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.
By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this work by incorporating a singular interaction that allows the effective symmetry to be tuned between the bosonic and fermionic limits. In this framework, the particles can be treated as subject to Haldane's generalized exclusion statistics. Solving the dynamics analytically using the framework of statistical anyons we explore the interplay between interparticle interactions and wave function symmetry on engine performance.
Abstract Heat engines convert thermal energy into mechanical work both in the classical and quantum regimes1. However, quantum theory offers genuine non-classical forms of energy, different from heat, which so far have not been exploited in cyclic engines. Here we experimentally realize a quantum many-body engine fuelled by the energy difference between fermionic and bosonic ensembles of ultracold particles that follows from the Pauli exclusion principle2. We employ a harmonically trapped superfluid gas of6Li atoms close to a magnetic Feshbach resonance3that allows us to effectively change the quantum statistics from Bose–Einstein to Fermi–Dirac, by tuning the gas between a Bose–Einstein condensate of bosonic molecules and a unitary Fermi gas (and back) through a magnetic field4–10. The quantum nature of such a Pauli engine is revealed by contrasting it with an engine in the classical thermal regime and with a purely interaction-driven device. We obtain a work output of several 106vibrational quanta per cycle with an efficiency of up to 25%. Our findings establish quantum statistics as a useful thermodynamic resource for work production.
The unavoidable irreversible losses of power in a heat engine are found to be of quantum origin. Following thermodynamic tradition a model quantum heat engine operating by the Otto cycle is analyzed. The working medium of the model is composed of an ensemble of harmonic oscillators. A link is established between the quantum observables and thermodynamical variables based on the concept of canonical invariance. These quantum variables are sufficient to determine the state of the system and with it all thermodynamical variables. Conditions for optimal work, power and entropy production show that maximum power is a compromise between the quasistatic limit of adiabatic following on the compression and expansion branches and a sudden limit of very short time allocation to these branches. At high temperatures and quasistatic operating conditions the efficiency at maximum power coincides with the endoreversible result. The optimal compression ratio varies from the square root of the temperature ratio in the quasistatic limit where their reversibility is dominated by heat conductance to the temperature ratio to the power of 1/4 in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.
Anyons are quasiparticles with quantum statistics interpolating between those of bosons and fermions. Two distinct manifestations of anyonic behaviour have been theoretically established: fractional exchange statistics where particle exchange can produce any phase, and generalized exclusion statistics which extends the Pauli exclusion principle. While anyons exhibiting fractional exchange statistics have been observed in diverse platforms, experimental realizations of generalized exclusion statistics and direct measurements of its thermodynamic signatures have remained elusive. Here, we realize an anyonic thermodynamic ensemble obeying generalized exclusion statistics and detect its anyonic thermodynamics in a one-dimensional strongly interacting quantum gas. To achieve this, we exploit the bijective mapping between dynamical and statistical interactions in one dimension. By tuning interaction strength and temperature over a wide range, we measure the equation of state and identify clear departures from Bose-Einstein and Fermi-Dirac statistics. These deviations are quantitatively captured by generalized exclusion statistics, providing direct evidence for the generalized Pauli principle. Independent probes of other thermodynamic quantities including pressure and the Tan contact further validate this framework. Our results establish a versatile platform for engineering anyonic exclusion statistics and open the door to thermodynamic applications of anyons in quantum technologies.