Sampurna Karmakar : Fractional Exclusion Statistics Driven Quantum Heat Engine

Abstract:

Haldane exclusion statistics (HES) provides a framework for continuously interpolating between bosons (g=0) and fermions (g=1) through a statistical interaction parameter g. We first identify an intrinsic particle-hole symmetry breaking in the Haldane-Wu distribution for $g \neq 1$, quantified by the deviation of its maximum entropy density from the free fermion value $k_B \ln 2$. This symmetry breaking gives rise to a finite thermoelectric response and consequently significant violations of the Wiedemann-Franz law. Next we investigate the role of fractional exclusion statistics in quantum heat engines, for which the maximum extractable power is constrained by the Whitney bound within the conventional fermionic framework. We demonstrate that this bound is not universal across quantum statistics: employing particles obeying HES allows this bound to be surpassed for g<1, with the enhancement reaching its extremal value in the bosonic limit. As an experimental realization, we further perform a microscopic numerical analysis of a quantum heat engine based on magnon transport through a ferromagnetic spin chain. Our results establish that quantum statistics can serve as an independent thermodynamic resource, opening up regimes of heat engine performance beyond conventional fermionic limitations.

References:

[1] F. D. M. Haldane, ‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle, Phys.Rev. Lett. 67, 937 (1991).

[2] Y.-S. Wu, Statistical Distribution for Generalized Ideal Gas of Fractional-Statistics Particles, Phys. Rev. Lett. 73,  922 (1994).

[3] S. Karmakar, A. Ratnakar, and S. Das, Statistical interaction driven thermoelectricity and violation of  Wiedemann-Franz law, arXiv:2506.01930.

[4] R. S. Whitney, Most efficient quantum thermoelectric at finite power output, Phys. Rev. Lett. 112, 130601 (2014).

[5] S. Karmakar, A. Hasan, and S. Das, Exclusion Statistics as a Thermodynamic Resource in Quantum Heat Engines, arXiv:2606.19310.