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arXiv · 2510.25533

Fundamental Work Scaling and Non-Extensivity in Critical Engines

Bastian Castorene·Martin HvE Groves·Francisco J. Peña·Eugenio E. Vogel·Patricio Vargas
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Abstract

We present a general analytical framework for critical two-isothermal engines that emerge operationally from quasi-static quantum Stirling cycles across ground-state level crossings (GLCs) in the low-temperature regime, where reversible heat exchange is governed by the structural entropy change while the internal energy remains constant. Within this ideal-reservoir, low-temperature equilibrium model, the Primarch Formula gives an exact quasistatic ensemble-average expression linking extracted work and efficiency directly to macroscopic ground-state degeneracies. In this reversible setting, the engines reach Carnot efficiency without a classical regenerator. For the perturbative population pattern analyzed here, thermal excitations reduce the ideal work and efficiency. Validated against exact numerical simulations of generalized \textit{N}-th spin-s 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 three distinct work-scaling regimes: persistent logarithmic non-extensivity, recovery of extensivity in the thermodynamic limit, and asymptotic extensivity with a logarithmic finite-size correction. In all three regimes, Carnot efficiency is attained within the reversible equilibrium model.

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Bastian Castorene, Martin HvE Groves, Francisco J. Peña, Eugenio E. Vogel, Patricio Vargas. 2025-10-29. Fundamental Work Scaling and Non-Extensivity in Critical Engines. https://arxiv.org/abs/2510.25533

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