Fundamental Work Scaling and Non-Extensivity in Critical Quantum Stirling Engines
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908932283301888 |
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| author | Castorene, Bastian Groves, Martin HvE Peña, Francisco J. Vogel, Eugenio E. Vargas, Patricio |
| author_facet | Castorene, Bastian Groves, Martin HvE Peña, Francisco J. Vogel, Eugenio E. Vargas, Patricio |
| contents | We present a general analytical framework for quasi-static quantum Stirling engines operating across ground-state level crossings (GLC). In the low-temperature regime, we derive the Primarch Formula, an exact universal expression linking extracted work and efficiency directly to macroscopic ground-state degeneracies. We analytically prove that these engines achieve Carnot efficiency without a classical regenerator, and that thermal excitations strictly degrade this performance. Validated against exact numerical simulations of generalized \textit{N}-th spin-1/2 Heisenberg models with nontrivial interactions, the framework is applied to the one-dimensional antiferromagnetic Ising model, revealing a profound connection to number theory. Governed by Fibonacci, Lucas, and parity-dependent critical degeneracies, the engine exhibits distinct operational regimes that permanently violate classical thermodynamic extensivity while operating at the absolute Carnot limit, regardless of macroscopic system size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental Work Scaling and Non-Extensivity in Critical Quantum Stirling Engines Castorene, Bastian Groves, Martin HvE Peña, Francisco J. Vogel, Eugenio E. Vargas, Patricio Statistical Mechanics We present a general analytical framework for quasi-static quantum Stirling engines operating across ground-state level crossings (GLC). In the low-temperature regime, we derive the Primarch Formula, an exact universal expression linking extracted work and efficiency directly to macroscopic ground-state degeneracies. We analytically prove that these engines achieve Carnot efficiency without a classical regenerator, and that thermal excitations strictly degrade this performance. Validated against exact numerical simulations of generalized \textit{N}-th spin-1/2 Heisenberg models with nontrivial interactions, the framework is applied to the one-dimensional antiferromagnetic Ising model, revealing a profound connection to number theory. Governed by Fibonacci, Lucas, and parity-dependent critical degeneracies, the engine exhibits distinct operational regimes that permanently violate classical thermodynamic extensivity while operating at the absolute Carnot limit, regardless of macroscopic system size. |
| title | Fundamental Work Scaling and Non-Extensivity in Critical Quantum Stirling Engines |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2510.25533 |