Francisco José Peña

Non-Hermitian band descriptions capture how loss, gain, and environmental coupling reshape quantum matter, yet most experimental probes remain wave based or dynamical. Here we develop an equilibrium charge-response route to spectral compression in Dirac materials. In the real-spectrum regime, invariance of the particle-number operator under the similarity transformation makes the quantum capacitance exactly that of the Hermitian partner, so the whole non-Hermitian content is carried by the Petermann factor. In a minimal nonreciprocal graphene model, hopping imbalance suppresses the Dirac velocity, enhancing the low-energy density of states and the capacitance as an exceptional point is approached. At charge neutrality the capacitance stays linear in temperature, with its slope enhanced relative to the Hermitian value. A perpendicular magnetic field recasts the same compression as a collapse of the Landau-level ladder, drawing more levels into the thermal window. In two dimensions, the capacitance enhancement relative to the Hermitian partner coincides exactly with the Petermann factor, even though the two have entirely different origins. This relation provides a controlled starting point for extending equilibrium thermodynamic probes to non-Hermitian electronic systems with interactions, disorder, and reservoir coupling.

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 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.

In this work, quantum Stirling engines based on monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene under perpendicular magnetic fields are analyzed. Performance maps of the useful work (ηW) reveal a robust optimum at low magnetic fields and moderately low temperatures, with all stackings capable of reaching Carnot efficiency under suitable configurations. The AB bilayer achieves this across the broadest parameter window while sustaining finite work, the monolayer exhibits highly constrained regimes, and the trilayer shows smoother trends with sizable ηW. These results identify multilayer graphene, particularly the AB bilayer, as a promising platform for efficient Stirling engines, while also highlighting the versatility of the monolayer in realizing all four operational regimes of the Stirling cycle.

In this work, we investigate the relationship between the Seebeck coefficient (S), and the differential entropy per particle (DEP, s), as a tool for characterizing charge carriers in two-dimensional systems. Using armchair silicene nanoribbons as a model platform, we analyze how both quantities and their ratio depend on chemical potential at room temperature. While the Seebeck coefficient captures transport properties through the energy dependence of the electronic transmission, the DEP is directly connected to the system's electronic entropy, offering a direct thermodynamic alternative for estimating S. We evaluate these transport-thermodynamic properties considering diverse ribbon widths, defining metallic and semiconducting regimes. We find both quantities S and s, are highly interconnected within the ribbon's band gap energy region, and their ratio s/S converges to the elementary charge e across that energy window, fulfilling the Kelvin formula S=s/e. On the contrary, s/S is undefined for gapless ribbons in the energy window of the first transmission channel. These results establish the ratio between the DEP and the Seebeck coefficient as a reliable and complementary probe for the determination of the elementary charge, and to identify the cleanness of electronic band gaps as s/S matches with e.

This work explores the thermodynamic performance of a quantum Stirling heat engine implemented with an anisotropic spin‐1 Heisenberg dimer as the working medium. Using the Hamiltonian of the system, the interplay of anisotropy, magnetic field, and exchange interactions and their influence is analyzed on the energy spectrum and the quantum level crossing. These results reveal that double‐degenerate point (DDP) and a triple‐degenerate point (TDP) play pivotal roles in shaping the operational regimes and efficiency of the quantum Stirling engine. At those points, the Carnot efficiency reaches higher work output and enhanced stability, making it a robust candidate for optimal thermodynamic performance. These findings highlight the potential of anisotropic spin systems as viable platforms for quantum heat engines and contribute to advancing the field of quantum thermodynamics.

We introduce a novel entropy-related function, non-repeatability, designed to capture dynamical behaviors in complex systems. Its normalized form, mutability, has been previously applied in statistical physics as a dynamical entropy measure associated with any observable stored in a sequential file. We now extend this concept by calculating the sorted mutability for the same data file previously ordered by increasing or decreasing value. 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, sorted mutability reveals additional insights into the critical behavior of the systems under study.

In this work, we investigate a system of three entangled qubits within the XXX model, subjected to an external magnetic field in the z direction and incorporating an anisotropy term along the y axis. We explore the system's thermodynamics by calculating its magnetic susceptibility and analyzing how this quantity encodes information about entanglement. By deriving rigorous bounds for the susceptibility, we demonstrate that violations of these bounds serve as an entanglement witness. Our results show that anisotropy enhances entanglement, extending the temperature range over which it persists. Furthermore, when the system is traced over the degrees of freedom of two qubits, the reduced entropy of the remaining single qubit corresponds to that of a system in a thermal bath with temperature T>0K.