| name | exclusion-statistics-thermodynamic-resource |
| category | quantum-physics |
| description | Haldane fractional exclusion statistics as tunable thermodynamic resource for quantum heat engines — bosonic working mediums exceed fermionic Whitney power limit by 1.52×. |
| trigger_words | exclusion statistics quantum heat engine, Haldane statistics thermodynamics, Whitney limit quantum, bosonic thermoelectric power, fractional exclusion statistics, quantum thermodynamic resource, anyonic thermodynamics |
Exclusion Statistics as a Thermodynamic Resource in Quantum Heat Engines
Source: arXiv:2606.19310 (Karmakar, Hasan, Das, June 2026)
Overview
The maximum power extractable from a quantum thermoelectric heat engine operating with free fermion carriers is bounded by the universal Whitney limit. This skill demonstrates that this bound is not fundamental — bosonic working mediums yield strictly enhanced maximum power, and Haldane fractional exclusion statistics provides a continuously tunable thermodynamic resource.
Core Methodology
1. The Whitney Limit is Fermion-Specific
For free fermion carriers:
- Maximum power: P_fermion^max ≈ 0.0321 × π² × kB² × (TL - TR)² / h
- This is NOT a fundamental limit of quantum heat engines
- It is an artifact of fermionic statistics
2. Bosonic Enhancement
For bosonic working mediums:
- Maximum power: P_boson^max = (ln 2)² × kB² × (TL - TR)² / h
- Exceeds fermionic limit by factor: (ln 2)² / (0.0321 × π²) ≈ 1.52×
- Proposed realization: magnon transport through a ferromagnetic spin chain
3. Haldane Fractional Exclusion Statistics
Using Haldane's exclusion statistics parameter g:
- Continuous interpolation between bosonic (g = 0) and fermionic (g = 1) limits
- Monotonic enhancement of maximum power for g < 1 at reduced bias cost
- Quantum statistical exclusion becomes a previously unrecognized and independently tunable thermodynamic resource
Key Results
| Statistics Type | Max Power Coefficient | Relative Performance |
|---|
| Fermionic (g=1) | 0.0321 × π² ≈ 0.317 | Baseline (Whitney limit) |
| Bosonic (g=0) | (ln 2)² ≈ 0.480 | 1.52× enhancement |
| Anyonic (0<g<1) | Between above | Continuously tunable |
Applications
- Quantum thermoelectric devices: Design heat engines beyond fermionic power limits
- Spin caloritronics: Magnon-based thermal transport in ferromagnets
- Quantum heat engines: Optimize working medium statistics for maximum power
- Thermal management: Use exclusion statistics as control parameter
Key Insights
- Statistics is a resource: Particle statistics can be independently tuned like temperature or voltage
- Bosons are more powerful: Same system, bosonic carriers → 52% more power than fermionic
- Experimental path exists: Magnon transport in ferromagnetic spin chains is a viable bosonic realization
- Continuous control: Haldane parameter g provides a knob between bosonic and fermionic performance
Pitfalls
- Whitney limit is not universal: Don't assume it applies to non-fermionic systems
- Bosonic realization requires specific platform: Magnon transport, not arbitrary bosonic systems
- Reduced bias cost: The power enhancement comes with a tradeoff in bias requirements
