arXiv subjects

Massimo Tessarotto

Publications and source records attributed to Massimo Tessarotto.

At least 19 recordsLinked to original sources

arXiv2025

A new type of Multiverse, G\"odel theorems and the nonstandard logic of classical, quantum mechanics and quantum gravity

The problem is posed of establishing a possible relationship between a new type of Multi-verse representation, G\"odel undecidability theorems and the logic of classical, quantum mechanics and quantum gravity. For this purpose example cases of multi-verses are first discussed in the context of non-relativistic classical, quantum mechanics and quantum gravity. As a result, it is confirmed that thanks to G\"odel theorems non-relativistic classical and quantum mechanics, as well as quantum gravity theory are incomplete. As a consequence, they necessarily admit undecidable logical propositions and therefore obey a three-way boolean logical, i.e., a propositional logic with the three different logical truth values true, false and undecidable.

physics.gen-ph↗

arXiv2024

The non-standad logic of physics: the case of the Boltzmann-Sinai hard-sphere system

One of the most challenging and fascinating issues in mathematical and theoretical physics concerns identifying the common logic, if any, which underlies the physical world. More precisely, this involves the search of the possibly-unique axiomatic logical proposition calculus to apply simultaneously both to classical and quantum realms of physics and to be consistent with the corresponding mathematical and filosophysical setups. Based on the recent establishment of quantum logic, which has been shown to apply both to Quantum Mechanics and Quantum Gravity, the crucial remaining step involves the identification of the appropriate axiomatic logical proposition calculus to be associated with Classical Mechanics. In this paper the issue is posed for a fundamental example of Classical Mechanics, which is represented by the so-called Boltzmann-Sinai dynamical system. This is realized by the ensemble of classical smooth hard-spheres, which is set at the basis of Classical Statistical Mechanics and is also commonly regarded as a possible realization of Classical Newtonian Cosmology. Depending on the initial conditions which are prescribed for such a system, its classical state is shown to obey the propositional calculus of non-classical logic. In particular, the latter is expressed by the 3-way Principle of Non-Contradiction, namely the same logical principle that holds for quantum logic. The result therefore permits to question on a mathematical basis the principles of deterministic classical logic and the validity of their character within the domain of Classical Physics. Such a conclusion represents a potential notable innovation in the logical dicotomy true/false, a crucial topic which has crossed millennia through philosophy, logic, mathematics and physics.

physics.class-ph↗

arXiv2023

On the conditions of validity of the Boltzmann equation and Boltzmann H-theorem

In this paper the problem is posed of the formulation of the so-called "ab initio" approach to the statistical description of the Boltzmann-Sinai N-body classical dynamical system (CDS) formed by identical smooth hard spheres. This amounts to introducing a suitably-generalized version of the axioms of Classical Statistical Mechanics. The latter involve a proper definition of the functional setting for the N-body probability density function (PDF), so that it includes also the case of the deterministic N-body PDF. In connection with this issue, a further development concerns the introduction of modified collision boundary conditions which differ from the usual ones adopted in previous literature. Both features are proved to be consistent with the validity of exact H-theorems for the N-body and 1-body PDFs respectively. Consequences of the axiomatic approach which concern the conditions of validity of the Boltzmann kinetic equation and the Boltzmann H-theorem are investigated. In particular, the role of the modified boundary conditions is discussed. It is shown that both theorems fail in the case in which the N-body PDF is identified with the deterministic PDF. Finally, the issue of applicability of the Zermelo and Loschmidt paradoxes to the "ab initio" approach presented here is discussed.

cond-mat.stat-mech↗

arXiv2023

Theory of spatially non-symmetric kinetic equilibria for collisionless plasmas

The problem posed by the possible existence/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas this involves the construction of stationary solutions of the Vlasov-Maxwell equations. In this paper the issue is addressed for non-relativistic plasmas both in astrophysical and laboratory contexts. The treatment is based on a Lagrangian variational description of single-particle dynamics. Starting point is a non-perturbative formulation of gyrokinetic theory, which allows one to construct "a posteriori" with prescribed order of accuracy an asymptotic representation for the magnetic moment. In terms of the relevant particle adiabatic invariants generalized bi-Maxwellian equilibria are proved to exist. These are shown to recover, under suitable assumptions, a Chapman-Enskog form which permits an analytical treatment of the corresponding fluid moments. In particular, the constrained posed by the Poisson and the Ampere equations are analyzed, both for quasi-neutral and non-neutral plasmas. The conditions of existence of the corresponding non-symmetric kinetic equilibria are investigated. As a notable feature, both astrophysical and laboratory plasmas are shown to exhibit, under suitable conditions, a kinetic dynamo, whereby the equilibrium magnetic field can be self-generated by the equilibrium plasma currents.

astro-ph.HE↗

arXiv2023

Collisionless kinetic regimes for quasi-stationary axisymmetric accretion disc plasmas

This paper is concerned with the kinetic treatment of quasi-stationary axisymmetric collisionless accretion disc plasmas. The conditions of validity of the kinetic description for non-relativistic magnetized and gravitationally-bound plasmas of this type are discussed. A classification of the possible collisionless plasma regimes which can arise in these systems is proposed, which can apply to accretion discs around both stellar-mass compact objects and galactic-center black holes. Two different classifications are determined, which are referred to respectively as energy-based and magnetic field-based classifications. Different regimes are pointed out for each plasma species, depending both on the relative magnitudes of kinetic and potential energies and the magnitude of the magnetic field. It is shown that in all cases, there can be quasi-stationary Maxwellian-like solutions of the Vlasov equation. The perturbative approach outlined here permits unique analytical determination of the functional form for the distribution function consistent, in each kinetic regime, with the explicit inclusion of finite Larmor radius-diamagnetic and/or energy-correction effects.

astro-ph.HE↗

arXiv2023

Kinetic equilibria of relativistic collisionless plasmas in the presence of non-stationary electromagnetic fields

The kinetic description of relativistic plasmas in the presence of time-varying and spatially non-uniform electromagnetic fields is a fundamental theoretical issue both in astrophysics and plasma physics. This refers, in particular, to the treatment of collisionless and strongly-magnetized plasmas in the presence of intense radiation sources. In this paper the problem is investigated in the framework of a covariant gyrokinetic treatment for Vlasov-Maxwell equilibria. The existence of a new class of kinetic equilibria is pointed out, which occur for spatially-symmetric systems. These equilibria are shown to exist in the presence of non-uniform background EM fields and curved space-time. In the non-relativistic limit this feature permits the determination of kinetic equilibria even for plasmas in which particle energy is not conserved due to the occurrence of explicitly time-dependent EM fields. Finally, absolute stability criteria are established which apply in the case of infinitesimal symmetric perturbations that can be either externally or internally produced.

astro-ph.HE↗

arXiv2023

Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas

Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidence suggest that magnetized plasmas of this type are collisionless and can persist for long times (e.g., with respect to a distant observer, coordinate, time), while exhibiting geometrical structures characterized by the absence of well-defined spatial symmetries. In this paper the problem is posed whether such configurations can correspond to some kind of kinetic equilibrium. The issue is addressed from a theoretical perspective in the framework of a covariant Vlasov statistical description, which relies on the method of invariants. For this purpose, a systematic covariant variational formulation of gyrokinetic theory is developed, which holds without requiring any symmetry condition on the background fields. As a result, an asymptotic representation of the relativistic particle magnetic moment is obtained from its formal exact solution, in terms of a suitably-defined invariant series expansion parameter (perturbative representation). On such a basis it is shown that spatially non-symmetric kinetic equilibria can actually be determined, an example being provided by Gaussian-like distributions. As an application, the physical mechanisms related to the occurrence of a non-vanishing equilibrium fluid 4-flow are investigated.

physics.plasm-ph↗

arXiv2023

Kinetic formulation of Tolman-Ehrenfest effect: Non-ideal fluids in Schwarzschild and Kerr space-times

A review of the original thermodynamic formulation of the Tolman-Ehrenfest effect prescribing the temperature profile of uncharged fluid at thermal equilibrium forming stationary configurations in curved space-time is proposed. A statistical description based on relativistic kinetic theory is implemented. In this context the Tolman-Ehrenfest relation arises in the Schwarzschild space-time for collisionless uncharged particles at Maxwellian kinetic equilibrium. However, the result changes considerably when non-ideal fluids, i.e., non-Maxwellian distributions, are treated, whose statistical temperature becomes non-isotropic and gives rise to a tensor pressure. This is associated with phase-space anisotropies in the distribution function, occurring both for diagonal and non-diagonal metric tensors, exemplified by the Schwarzschild and Kerr metrics respectively. As a consequence, it is shown that for these systems it is not possible to define a Tolman-Ehrenfest relation in terms of an isotropic scalar temperature. Qualitative properties of the novel solution are discussed.

gr-qc↗

arXiv2023

Polytropic representation of the kinetic pressure tensor of non-ideal magnetized fluids in equilibrium toroidal structures

Non-ideal fluids are generally subject to the occurrence of non-isotropic pressure tensors, whose determination is fundamental in order to characterize their dynamical and thermodynamical properties. This requires the implementation of theoretical frameworks provided by appropriate microscopic and statistical kinetic approaches in terms of which continuum fluid fields are obtained. In this paper the case of non-relativistic magnetized fluids forming equilibrium toroidal structures in external gravitational fields is considered. Analytical solutions for the kinetic distribution function are explicitly constructed, to be represented by a Chapman-Enskog expansion around a Maxwellian equilibrium. In this way, different physical mechanisms responsible for the generation of non-isotropic pressures are identified and proved to be associated with the kinetic constraints imposed on single and collective particle dynamics by phase-space symmetries and magnetic field. As a major outcome, the validity of a polytropic representation for the kinetic pressure tensors corresponding to each source of anisotropy is established, whereby directional pressures exhibit a specific power-law functional dependence on fluid density. The astrophysical relevance of the solution for the understanding of fluid plasma properties in accretion-disc environments is discussed.

physics.plasm-ph↗

arXiv2018

Macroscopic irreversibility and decay to kinetic equilibrium of the 1-body PDF for finite hard-sphere systems

The conditions for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the 1-body probability density function (PDF) associated with hard-sphere systems are investigated. The problem is set in the framework of the axiomatic "ab initio" theory of classical statistical mechanics developed recently and the related establishment of an exact kinetic equation realized by the Master equation for the same kinetic PDF. As shown in the paper the task involves the introduction of a suitable functional of the 1-body PDF, identified here with the Master kinetic information. It is then proved that, provided the same PDF is prescribed in terms of suitably-smooth, i.e., stochastic, solution of the Master kinetic equation, the two properties indicated above are indeed realized.

math-ph↗

arXiv2018

Generalized Lagrangian Path approach to manifestly-covariant quantum gravity theory

A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory) proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant are determined in such a framework, which exhibit Gaussian-like probability densities that are non-dispersive in proper-time. As a remarkable outcome of the theory achieved by implementing these analytical solutions, the existence of an emergent gravity phenomenon is proved to hold. Accordingly, it is shown that a mean-field background space-time metric tensor can be expressed in terms of a suitable statistical average of stochastic fluctuations of the quantum gravitational field whose quantum-wave dynamics is described by GLP trajectories.

gr-qc↗

arXiv2018

Space-time second-quantization effects and the quantum origin of cosmological constant in covariant quantum gravity

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

gr-qc↗

arXiv2017

Quantum-wave equation and Heisenberg inequalities of covariant quantum gravity

Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015-2017) are investigated. These refer, first, to the establishment of the 4-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG) wave equation, which advances the quantum state $ψ$ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton-Jacobi quantization of the classical variational tensor field $g\equiv \left\{ g_{μν}\right\} $ and its conjugate momentum, referred to as (canonical) $g-$quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for $ψ$, which provide an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state $ψ$ is proved to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the matric tensor $g\equiv \left\{ g_{μν}\right\} $ and its quantum conjugate momentum operator.

gr-qc↗

arXiv2017

Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor $\widehat{g}(r)\equiv \left\{ \widehat{g}_{μν}(r)\right\} $ solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields $x\equiv \left\{ g,π\right\} $ obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations$.$ It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably-reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly-covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

gr-qc↗

arXiv2017

Hamiltonian approach to GR - Part 2: covariant theory of quantum gravity

A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly-covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave-function are realized in $% 4-$scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the $4-$scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant.

gr-qc↗

arXiv2017

Macroscopic irreversibility and decay to kinetic equilibrium for classical hard-sphere systems

In this paper the conditions are investigated for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the $1-$body probability density function (PDF) associated with hard-sphere systems. The problem is set in the framework of the axiomatic "ab initio" approach to classical statistical mechanics recently developed [Tessarotto \textit{et al}., 2013-2017] and the related establishment of an exact kinetic equation realized by Master equation for the same kinetic PDF. As shown in the paper the task involves the introduction of a suitable functional of the $1-$body PDF here identified with the \textit{Master kinetic information}. The goal is to show that, provided the same PDF is realized in terms of an arbitrary suitably-smooth particular solution of the Master kinetic equation the two properties indicated above are indeed realized and that the same functional is unrelated either with the Boltzmann-Shannon entropy and the Fisher information.

physics.class-ph↗

arXiv2017

Asymptotic orderings and approximations of the Master kinetic equation for large hard spheres systems

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large $N-$body system of hard spheres,\textit{ i.e.,} formed by $N\equiv\frac{1}{\varepsilon} \gg1$ particles, which are allowed to undergo instantaneous and purely elastic unary, binary or multiple collisions. Starting point is the axiomatic treatment recently developed [Tessarotto \textit{et al}., 2013-2016] and the related discovery of an exact kinetic equation realized by Master equation which advances in time the $1-$body probability density function (PDF) for such a system. As shown in the paper the task involves introducing appropriate asymptotic orderings in terms of $\varepsilon$ for all the physically-relevant parameters. The goal is that of identifying the relevant physically-meaningful asymptotic approximations applicable for the Master kinetic equation, together with their possible relationships with the Boltzmann and Enskog kinetic equations, and holding in appropriate asymptotic regimes. These correspond either to dilute or dense systems and are formed either by small-size or finite-size identical hard spheres, the distinction between the various cases depending on suitable asymptotic orderings in terms of $\varepsilon.$

physics.class-ph↗

arXiv2016

Principles of kinetic theory for granular fluids

Highlights are presented regarding recent developments of the kinetic theory of granular matter. These concern the discovery of an exact kinetic equation and a related exact H-theorem both holding for finite $N-$body systems formed by smooth hard-spheres systems.

cond-mat.stat-mech↗