arXiv subjects

Eugenio E. Vogel

Publications and source records attributed to Eugenio E. Vogel.

3 recordsLinked to original sources

arXiv2026

Fundamental Work Scaling and Non-Extensivity in Critical Engines

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.

cond-mat.stat-mech↗

arXiv2025

Entropy alternatives for equilibrium and out of equilibrium systems

We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a dynamical entropy measure. To present the scope and advantages of these quantities, we analyze two distinct systems: (a) Monte Carlo simulations of magnetic moments on a square lattice and (b) seismic time series from the United States Geological Survey catalog. Both systems are well-established in the literature, serving as robust benchmarks. Shannon entropy is employed as a reference point to assess the similarities and differences with the proposed measures. A key distinction lies in the sensitivity of non-repeatability and mutability to the temporal ordering of data, which contrasts with traditional entropy definitions. Moreover, \textit{sorted mutability} -- the mutability computed from a reordered data version -- reveals additional insights into the critical behavior of the systems under study.

cond-mat.stat-mech↗

arXiv2024

Magnetocaloric effect for a $Q$-clock type system

In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with $Q$ possible orientations, known as the ``$Q$-state clock model". When the $Q$-state clock model has $Q\geq 5$ possible configurations, it presents the famous Berezinskii Kosterlitz Thouless (BKT) phase associated with vortices states. We calculate thermodynamic quantities using Monte Carlo simulations for even $Q$ numbers, ranging from $Q=2$ to $Q=8$ spin orientations per site in a lattice. We use lattices of different sizes with $L\times L = 8^{2}, 16^{2}, 32^{2}, 64^{2}, \text{and}\ 128^{2}$ sites, considering free boundary conditions and an external magnetic field varying between $B = 0$ and $B=1$ in natural units of the system. By obtaining the entropy, it is possible to quantify the MCE through an isothermal process in which the external magnetic field on the spin system is varied. In particular, we find the values of $Q$ that maximize the MCE depending on the lattice size and the magnetic phase transitions linked with the process. Given the broader relevance of the $Q$-state clock model in areas such as percolation theory, neural networks, and biological systems, where multi-state interactions are essential, our study provides a robust framework in applied quantum mechanics, statistical mechanics and related fields.

cond-mat.stat-mech↗