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.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.

cond-mat.mes-hallCross-listedarXiv:2606.19310Jun 18, 2026

Notes on Fermi and Bose Statistics

Morikazu TODA, Fumihiko TAKANO

Total mean curvature and submanifolds of finite typeOct 1, 19930 citations

Particle exchange statistics beyond fermions and bosons

Zhiyuan Wang, Kaden R. A. Hazzard

Abstract It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimensions 1–5 . In principle, a second exception known as parastatistics, which extends outside two dimensions, has been considered 6 but was believed to be physically equivalent to fermions and bosons 7–9 . Here we show that non-trivial parastatistics inequivalent to either fermions or bosons can exist in physical systems. These new types of identical particle obey generalized exclusion principles, leading to exotic free-particle thermodynamics distinct from any system of free fermions and bosons. We formulate our theory by developing a second quantization of paraparticles that naturally includes exactly solvable non-interacting theories and incorporates physical constraints such as locality. We then construct a family of exactly solvable quantum spin models in one and two dimensions, in which free paraparticles emerge as quasiparticle excitations, and their exchange statistics can be physically observed and are notably distinct from fermions and bosons. This demonstrates the possibility of a new type of quasiparticle in condensed matter systems and—more speculatively—the potential for previously unconsidered types of elementary particle.Abstract It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimensions 1–5 . In principle, a second exception known as parastatistics, which extends outside two dimensions, has been considered 6 but was believed to be physically equivalent to fermions and bosons 7–9 . Here we show that non-trivial parastatistics inequivalent to either fermions or bosons can exist in physical systems. These new types of identical particle obey generalized exclusion principles, leading to exotic free-particle thermodynamics distinct from any system of free fermions and bosons. We formulate our theory by developing a second quantization of paraparticles that naturally includes exactly solvable non-interacting theories and incorporates physical constraints such as locality. We then construct a family of exactly solvable quantum spin models in one and two dimensions, in which free paraparticles emerge as quasiparticle excitations, and their exchange statistics can be physically observed and are notably distinct from fermions and bosons. This demonstrates the possibility of a new type of quasiparticle in condensed matter systems and—more speculatively—the potential for previously unconsidered types of elementary particle.

arXiv:2308.05203NatureJan 8, 202532 citations

Fermi-Dirac statistics

S. Chaturvedi, Shyamal Biswas

ResonanceJan 1, 20146 citations

Quantum Heat Engines with Contact Interactions

Nathan M. Myers, Jacob McCready, Sebastian Deffner

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.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.

Apr 30, 20210 citations

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.