arXiv subjects

Giorgio Sonnino

Publications and source records attributed to Giorgio Sonnino.

At least 19 recordsLinked to original sources

arXiv2026

Extreme Kerr Newman Black Holes: Differential Geometry, Symmetry, and the Golden Ratio

We investigate the geometry of extreme Kerr-Newman black holes and its role in selecting distinct black hole states. Motivated by Smarr's question of what physical information is encoded in event-horizon symmetries, we identify, besides the Smarr extreme family, a special family in which the mass, charge, angular momentum, and irreducible mass are constrained by a single irrational number. In the Christodoulou diagram, this family is selected by a discrete symmetry of appropriately scaled charge and angular-momentum variables. The local differential geometry of the event horizon provides an additional selection principle, which, up to the discrete symmetries (Q \rightarrow\pm Q) and (J \rightarrow\pm J), identifies a unique extreme Kerr-Newman black hole exhibiting the highest degree of local spherical symmetry compatible with the rotating Kerr-Newman geometry. Remarkably, for this distinct extreme configuration, all relevant physical and geometrical quantities, including the energy, electric charge, angular momentum, and irreducible mass, are solely related through the golden ratio. We also examine reversible and irreversible transformations and the associated extractable energy. Intrinsic horizon geometry can therefore constrain the macroscopic parameters and single out distinct extreme Kerr-Newman configurations.

astro-ph.GA↗

arXiv2026

Emergent Spinorial Structure in Mesoscopic Irreversible Thermodynamics

We reconstruct a geometry of thermodynamic coordinates from transport coefficients within a mesoscopic canonical model. Self-adjoint flux observables determine a compatible evolution generator containing symmetric and antisymmetric transport coefficients. When the Hermitian transport tensor is positive, an exact graded first-order factorization reproduces this generator on its scalar sector. Its commutators define a spectral distance whose metric depends only on the symmetric tensor. Gradients of the antisymmetric tensor can change the evolution while leaving the metric unchanged. The construction allows coordinate-dependent coefficients. In the constant Onsager regime, a Clifford representation gives the same distance and an algebra fixed by the transport matrix. Published transport data for a $\mathrm{Bi_2Te_3}$ film give a principal-distance ratio of approximately $2.12$ in normalized coordinates at $ZT\simeq0.68$. We also examine a separate quadratic entropy-production observable and distinguish its discrete spectrum from the spectrum of the evolution generator. The spinorial representation adds no physical spin degrees of freedom.

cond-mat.mes-hall↗

arXiv2026

Transport Determines Spectral Distance in Mesoscopic Thermodynamics

We derive a distance between thermodynamic states from a positive Hermitian transport tensor within a mesoscopic canonical model. An exact first-order factorization of the evolution generator gives a commutator norm and the metric $G=2g^{-1}$, where $g$ denotes the symmetric transport tensor. Gradients of the antisymmetric tensor can change the evolution, but they leave this distance unchanged. The construction allows coordinate-dependent coefficients. For constant Onsager coefficients, a Clifford representation gives the same metric. In a two-channel thermoelectric system, the ratio of normalized principal distances is $\sqrt{1+ZT}+\sqrt{ZT}$. Transport coupling thus fixes the anisotropy of this metric. The construction requires neither an independent metric nor a physical spin variable.

cond-mat.mes-hall↗

arXiv2026

Gravity, Entropy, and the Second Law: A Pedagogical Perspective

An interesting question for discussion in university physics courses is whether gravity can conflict with the second law of thermodynamics. In this work, we address this question by comparing the behavior of an ideal gas in two conceptually different regimes: one in which gravitational effects can be neglected and another in which self-gravity becomes important. In the first case, free expansion provides the familiar example in which an increase in the volume accessible to the gas leads to an increase in entropy. Self-gravitating systems behave differently: gravitational contraction can reduce the volume occupied by matter while releasing energy and increasing the entropy of the surroundings. This illustrates why the usual intuition that increasing entropy necessarily corresponds to increasing spatial dispersion cannot be applied directly to self-gravitating systems. Using elementary thermodynamic arguments and a minimal amount of mathematics, we discuss this apparent tension and show how entropy must be considered for the complete system, including emitted radiation. The discussion is finally extended to black holes and Hawking radiation, where the appropriate framework is the generalized second law of thermodynamics. The analysis is intended to provide a pedagogical bridge between elementary thermodynamics and some of the distinctive thermodynamic properties of gravitating systems.

physics.gen-ph↗

arXiv2026

Irreducible-Mass Balance for Magnetized Null Horizons with an Internal Current Sheet

We begin with a general question: how does the irreducible mass of a magnetized black hole change when the horizon is not stationary? The null Raychaudhuri equation gives an exact area balance for any smooth null horizon, without assuming stationarity or axisymmetry. When the horizon is axisymmetric and admits an integrable quasilocal Hamiltonian, this geometrical identity becomes an energy balance. The equation keeps area growth, rotational and electromagnetic work, nonstationary focusing, canonical-flux corrections, and internal-boundary terms separate. We then turn to Wang's self-gravitating split-monopole Blandford-Znajek engine. In the weak-field and slow-rotation regime, P/M_H\ll1 and a/M_H\ll1, our general balance reproduces Wang's mass- and angular-momentum loss rates. The irreducible mass, M_{irr}=\sqrt{A_H/(16π)}, reveals what those rates do not show by themselves. It measures the part of the rotational work absorbed irreversibly by the horizon. At fixed magnetic flux and under impedance matching, half of the instantaneous rotational work leaves as electromagnetic power. The other half increases the horizon area and M_{irr}. The assumptions behind this reduction are derived explicitly. A minimal nondissipative world-volume action makes the current-sheet contribution vanish through O(p^2ε^2). Direct power counting of Wang's perturbative fields, together with a compatible canonical-flux prescription, gives a relative focusing and canonical correction of O(p^2)+O(ε^2). These estimates mark the range in which the reduced Blandford-Znajek trajectory remains controlled. Extending that trajectory to high spin requires an additional extrapolation. Relating the quasilocal horizon loss to energy measured at infinity requires a separate asymptotic flux calculation.

astro-ph.GA↗

arXiv2026

Irreducible-Mass Growth and Extractable Energy in a Self-Gravitating Blandford-Znajek Engine

Wang recently constructed a self-gravitating split-monopole Blandford-Znajek engine and obtained its secular horizon mass and angular-momentum loss rates. We determine the previously unknown consequences of this evolution: the growth of the irreducible mass, the division of rotational work between outgoing electromagnetic power and horizon dissipation, and the lifetime-integrated energy removed from the horizon. For fixed magnetic flux and impedance matching, one half of the instantaneous rotational work is carried outward, and one half irreversibly increases the horizon area. Integrating Wang's spin-down trajectory, we find in the weak-field limit the exact results A_f/A_0=\sqrt{e} and E_{extr}^H/(M_{H,0}c^2)=1-exp{1/4}/\sqrt{2}\simeq 0.09206. The leading maximum-power spin-flux allocation instead gives E_{\rm extr}^{H}/(M_{H,0}c^2)\simeq 0.04668. These results provide the first irreducible-mass and extractable-energy accounting of Wang's engine. Their extension from quasilocal horizon quantities to energy received at infinity requires a separate flux analysis.

astro-ph.GA↗

arXiv2026

Entropy, Gravity, and an Apparent Violation of the Second Law

An interesting question to explore in physics classes is whether gravity violates the second law of thermodynamics. Standard physics textbooks provide little to no discussion of the relationship between entropy and gravity, and the same is often true of specialized texts. The aim of this work is to address this question by analyzing the behavior of an ideal gas in two simple scenarios: one in which gravity is negligible and another in which its effects are significant. We show that although systems influenced by gravity may exhibit counterintuitive behavior, such as local ordering through structure formation, the second law of thermodynamics remains valid when the entire system is considered, including all emitted energy and radiation. Given the educational focus of this work and the complexity of the entropy-gravity relationship, we omit detailed calculations that are not strictly necessary and instead focus on the simplest physical scenarios. In this context, we analyze four representative examples through simple calculations: the Sun, the limit of extreme contraction in black holes, the protostellar contraction sequence, and core collapse with neutrino cooling.

physics.gen-ph↗

arXiv2024

An Attempt to Derive the Expression of the Constant in the Thermodynamic Uncertainty Relations by a Statistical Model for a Quasi-Ideal Nano-Gas

In recent work, we have shown that fundamental quantities such as the total entropy production, the thermodynamic variables conjugate to the thermodynamic forces, and the Glansdorff-Prigogine's dissipative variable may be discretized at the mesoscopic scale. The Canonical Commutation Rules (CCRs) valid at the mesoscopic scale have been postulated and the measurement process consists of determining the eigenvalues of the operators associated with the thermodynamic quantities. The essence of that work was to analyze the consequences of these postulates. This letter aims to understand the physical nature of the new constant (beta) introduced in the CCRs. In particular, two questions are still open. Is beta a new fundamental constant? Does the constant in the CCRs correspond to the lowest limit? We shall tackle the problem starting from the simplest assumption: the expression of beta can be derived from a simple model (a heuristic model) for nano-gas and studied through the tools of classical statistical physics. We will find that the theoretical value is very close to the experimental one. We shall not go further in our interpretation; we shall limit ourselves simply by noticing that according to our model, the constant beta does not appear to be a new fundamental constant but corresponds to the minimum value.

cond-mat.mes-hall↗

arXiv2024

Surface Geometry of Some Meaningful Extreme Kerr-Newman Black Holes

We address the properties of extremal black holes by considering the Christodoulou-Ruffini/Hawking mass-energy formula. By simple geometrical arguments, we found that the mass/energy formula is satisfied by two meaningful extremal black holes where mass (m), charge (Q), and angular momentum/spin (L) are proportional to the black holes irreducible mass (m_{ir}) expressed by irrational numbers. These black holes have been studied in the Christodoulou diagram and their topology in E^3 has been investigated by differential geometry. We show that one of the analyzed Kerr-Newman black holes corresponds to the case where the Gaussian curvature becomes zero at the poles. in the first case, the coefficients are linked to irrational numbers. In the second extremal black hole examined, the fundamental quantities m, Q, and L are linked to the irreducible mass by coefficients that depend solely on the "golden ratio number" -ϕ_-. In this case, we show that if this extremal black hole satisfies the Pythagorean fundamental forms relation at the umbilic points, then both the scale parameter (corresponding to twice the irreducible mass) and the Gauss curvature of the surface at the poles are equal to the golden ratio numbers. For these two extremal black holes, we calculate the energy extractible by reversible transformations finding that, in percentage, the energy extractable from the latter black hole is higher than the former one.

gr-qc↗

arXiv2023

Uncertainty Relations in Thermodynamics of Irreversible Processes on a Mesoscopic Scale

Studies of mesoscopic structures have now become a leading and rapidly evolving research field ranging from physics, chemistry, and mineralogy to life sciences. The increasing miniaturization of devices with length scales of a few nanometers is leading to radical changes not only in the realization of new materials but also in shedding light on our understanding of the fundamental laws of nature that govern the dynamics of systems at the mesoscopic scale. On the basis of recent experimental results and previous theoretical research, we investigate thermodynamic processes in small systems in Onsager's region. We show that fundamental quantities such as the total entropy production, the thermodynamic variables conjugate to the thermodynamic forces, and the Glansdorff-Prigogine's dissipative variable may be discretized at the mesoscopic scale. We establish the canonical commutation rules (ccr) valid at the mesoscopic scale. The numerical value of the discretization constant is estimated experimentally. The ultraviolet divergence problem is solved by applying the correspondence principle with Einstein-Prigogine's fluctuations theory in the limit of macroscopic sy

cond-mat.mes-hall↗

arXiv2022

Turbulent Transport in Tokamak-plasmas: A Thermodynamic Approach

In previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients for systems out of Onsager's region. Since the proposed PDEs are obtained without neglecting any term present in the balance equations (i.e., the mass, momentum, and energy balance equations), we propose them as a good candidate for describing also transport in thermodynamic systems in turbulent regimes. As a special case, we derive the nonlinear PDEs for transport coefficients when the thermodynamic system is subjected to two thermodynamic forces. In this case, the obtained PDE is, in thermodynamical field theory (TFT), analogous to Liouville's equation in Riemannian (or pseudo-Riemannian) geometry. The validity of our model is tested by analyzing a concrete example where Onsager's relations manifestly disagree with experience: transport in Tokamak-plasmas. More specifically, we compute the electron mass and energy losses in turbulent FTU (Frascati Tokamak Upgrade)-plasmas. We show the agreement between the theoretical predictions and experimental observations. This approach allows for predicting the values of the Bohm and the gyro-Bohm coefficients. To the best of our knowledge, it is the first time that such coefficients have been evaluated analytically. The aim of this series of works is to apply our approach to the Divertor Tokamak Test facility (DTT), to be built in Italy, and to ITER.

physics.plasm-ph↗

arXiv2022

Efficient Multiparty Protocols Using Generalized Parseval's Identity and the Theta Algebra

We propose a protocol able to show publicly addition and multiplication on secretly shared values. To this aim we developed a protocol based on the use of masks and on the FMPC (Fourier Multi-Party Computation). FMPC is a novel multiparty computation protocol of arithmetic circuits based on secret-sharing, capable to compute addition and multiplication of secrets with no communication. We achieve this task by introducing the first generalisation of Parseval's identity for Fourier series applicable to an arbitrary number of inputs and a new algebra referred to as the "Theta-algebra". FMPC operates in a setting where users wish to compute a function over some secret inputs by submitting the computation to a set of nodes, without revealing them those inputs. FMPC offloads most of the computational complexity to the end users, and includes an online phase that mainly consists of each node locally evaluating specific functions. FMPC paves the way for a new kind of multiparty computation protocols; making it possible to compute addition and multiplication of secrets stepping away from circuit garbling and the traditional algebra introduced by Donald Beaver in 1991. Our protocol is capable to compute addition and multiplication with no communication and its simplicity provides efficiency and ease of implementation.

cs.CR↗

arXiv2022

Modelling the Spread of SARS-CoV2 and its variants. Comparison with Real Data. Relations that have to be Satisfied to Achieve the Total Regression of the SARS-CoV2 Infection

This work provides an overview on deterministic and stochastic models that have previously been proposed by us to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Europe and USA. Briefly, we describe realistic deterministic and stochastic models for the evolution of the COVID-19 pandemic, subject to the lockdown and quarantine measures, which take into account the time-delay for recovery or death processes. Realistic dynamic equations for the entire process have been derived by adopting the so-called "kinetic-type reactions approach". The lockdown and the quarantine measures are modelled by some kind of inhibitor reactions where susceptible and infected individuals can be "trapped" into inactive states. The dynamics for the recovered people is obtained by accounting people who are only traced back to hospitalised infected people. To model the role of the Hospitals we take inspiration from the Michaelis-Menten's enzyme-substrate reaction model (the so-called "MM reaction") where the "enzyme" is associated to the "available hospital beds", the "substrate" to the "infected people", and the "product" to the "recovered people", respectively. The statistical properties of the models, in particular the relevant correlation functions and the probability density functions, have duly been evaluated. We validate our theoretical predictions with a large series of experimental data for Italy, Germany, France, Belgium and United States, and we also compare data for Italy and Belgium with the theoretical predictions of the logistic model. We found that our predictions are in good agreement with the real world since the onset of COVID 19, contrary to the the logistics model that only applies in the first days of the pandemic. In the final part of the work, we can find the (theoretical) relationships that should be satisfied to obtain the disappearance of the virus.

q-bio.PE↗

arXiv2022

Thermodynamic Flux-Force Closure Relations for Systems out of the Onsager Region

The objective of this work is to determine the nonlinear flux-force relations for systems out of Onsager's region that respect the existing thermodynamic theorems for systems far from equilibrium. To this aim, a thermodynamic theory for irreversible processes [referred to as the Thermodynamical Field Theory (TFT)] has been developed. The TFT rests upon the concept of equivalence between thermodynamic systems: "The equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the entropy production and the Glansdorff-Prigogine dissipative quantity remain unaltered under the thermodynamic forces transformation". The TCT leads naturally to the "Thermodynamic Covariance Principle" (TCP) stating that "The nonlinear closure equations, i.e., the flux-force relations, must be covariant under TCT". In this work, we provide the explicit expression of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients when the skew-symmetric piece is absent. The solution of these equations allows to determine the flux-force closure relations for systems out of the Onsager region. Since the proposed PDEs are obtained without neglecting any term present in the balance equations (i.e., the mass, momentum, and energy balance equations), we propose them as a good candidate for describing transport in thermodynamic systems also in turbulent regime. A preliminary test is carried out by analysing a concrete example where Onsager's relations manifestly disagree with experience: losses in magnetically confined Tokamak-plasmas in fully collisional and in turbulent regimes. We show the good agreement between the theoretical predictions and the experimental data. The aim is to apply our approach to the "Divertor Tokamak Test facility" (DTT), to be built in Italy, and to ITER.

physics.plasm-ph↗

arXiv2022

Simple algorithm for GCD of polynomials

Based on the Bezout approach we propose a simple algorithm to determine the {\tt gcd} of two polynomials which doesn't need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The algorithm needs only $n$ steps for polynomials of degree $n$. Formal manipulations give the discriminant or the resultant for any degree without needing division nor determinant calculation.

cs.SC↗

arXiv2021

Modelling the Spreading of the SARS-CoV-2 in Presence of the Lockdown and Quarantine Measures by a "Kinetic-Type Reactions" Approach

We propose a realistic model for the evolution of the COVID-19 pandemic subject to the lockdown and quarantine measures, which takes into account the time-delay for recovery or death processes. The dynamic equations for the entire process are derived by adopting a kinetic-type reaction approach. More specifically, the lockdown and the quarantine measures are modelled by some kind of inhibitor reactions where susceptible and infected individuals can be trapped into inactive states. The dynamics for the recovered people is obtained by accounting people who are only traced back to hospitalised infected people. To get the evolution equation we take inspiration from the Michaelis- Menten enzyme-substrate reaction model (the so-called MM reaction) where the enzyme is associated to the available hospital beds, the substrate to the infected people, and the product to the recovered people, respectively. In other words, everything happens as if the hospitals beds act as a catalyser in the hospital recovery process. Of course, in our case the reverse MM reactions has no sense in our case and, consequently, the kinetic constant is equal to zero. Finally, the O.D.E.s for people tested positive to COVID-19 is simply modelled by the following kinetic scheme S+I=>2I with I=>R or I=>D, with S, I, R, and D denoting the compartments Susceptible, Infected, Recovered, and Deceased people, respectively. The resulting kinetic-type equation} provide the O.D.E.s, for elementary reaction steps, describing the number of the infected people, the total number of the recovered people previously hospitalised, subject to the lockdown and the quarantine measure, and the total number of deaths. The model foresees also the second wave of Infection by Coronavirus. The tests carried out on real data for Belgium, France and Germany confirmed the correctness of our model.

physics.med-ph↗

arXiv2020

A Stochastic Compartmental Model for COVID-19

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density function, have duly been computed. Our models, which generalises a model previously proposed and published in a specialised journal, take into account the adoption of the lockdown measures as well as the crucial role of the hospitals and Health Care Institutes. To accomplish this work we have analysed two scenarios: the SIS-model (Susceptible => Infectious => Susceptible) in presence of the lockdown measures and the SIS-model integrated with the action of the hospitals (always in presence of the lockdown measures). We show that in the case of the pure SIS-model, once the lockdown measures are removed, the Coronavirus will start growing again. However, in the second scenario, beyond a certain threshold of the hospital capacities, the Coronavirus is not only kept under control, but its capacity to spread tends to diminish in time. Therefore, the combined effect of the lockdown measures with the action of the hospitals and health Institutes is able to contain and dampen the spread of the SARS-CoV-2 epidemic. This result can be used during a period of time when the massive distribution of delivery of a limited number of vaccines in a given population is not yet feasible. By way of example, we analysed the data for USA and France where the intensities of the noise have been estimated by Statistical Mechanics. In particular, for USA we have analysed two possible hypotheses: USA is still subject to the first wave of infection by and USA is in the second (or third) wave of SARS-CoV-2 infection.The agreement between theoretical predictions and real data confirms the validity of our approach.

physics.med-ph↗

arXiv2020

Dynamics of the COVID-1 -- Comparison between the Theoretical Predictions and the Real Data, and Predictions about Returning to Normal Life

A new coronavirus disease, called COVID-19, appeared in the Chinese region of Wuhan at the end of last year; since then the virus spread to other countries, including most of Europe. We propose a differential equation governing the evolution of the COVID-19. This dynamic equation also describes the evolution of the number of infected people for 13 common respiratory viruses (including the SARS-CoV-2). We validate our theoretical predictions with experimental data for Italy, Belgium and Luxembourg, and compare them with the predictions of the logistic model. We find that our predictions are in good agreement with the real world since the beginning of the appearance of the COVID-19; this is not the case for the logistic model that only applies to the first days. The second part of the work is devoted to modelling the descending phase, i.e. the decrease of the number of people tested positive for COVID-19. Also in this case, we propose a new set of dynamic differential equations that we solved numerically. We use our differential equations parametrised with experimental data to make several predictions, such as the date when Italy, Belgium, and Luxembourg will reach a peak number of SARS-CoV-2 infected people. The descending curves provide valuable information such as the duration of the COVID-19 epidemic in a given Country and therefore when it will be possible to return to normal life. The study of the the dynamics of COVID-19 when the population have been subject to less restrictive measures is beyond the scope of this work and it will be matter of future works.

q-bio.PE↗