P. Ván

Wigner Research Centre for Physics

Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given. The usual basic fields of mass, momentum, energy and their c...

Variational principles play a fundamental role in deriving the evolution equations of physics. They work well in the case of non-dissipative evolution, but for dissipative systems, the variational principles are not unique and not constructive. With the methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipat...

Discovery of a novel thermodynamic aspect of nonrelativistic gravity is reported. Here, initially, an unspecified scalar field potential is considered and treated not as an externally applied field but as a thermodynamic variable on an equal footing with the fluid variables. It is shown that the second law of thermodynamics imposes a stringent cons...

Quantum mechanics, superfluids, and capillary fluids are closely related: It is thermodynamics that links them. In this paper, the Liu procedure is used to analyze the thermodynamic requirements. A comparison with the traditional method of divergence separation highlights the role of spacetime. It is shown that perfect Korteweg fluids are holograph...

Results of heat pulse experiments in various artificial and natural materials are reported in the paper. The experiments are performed at room temperature with macroscopic samples. It is shown that temperature evolution does not follow the Fourier's law but well explained by the Guyer-Krumhansl equation. The observations confirm the ability of non-...

We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals' thermodynamic model, whose equation of state features well-known terms that account for molecular attraction and size. The...

The rotational velocity curve (RC) of galaxy NGC 3198 is modelled in various theoretical frameworks: Thermodynamic Gravity (TG) is compared to Dark Matter (DM) and Modified Newtonian Dynamics (MOND). The nonlinear gravitational field equation of TG is solved using the baryonic mass density as the source of the gravitational field. In this paper, fi...

Quantum mechanics, superfluids and capillary fluids are closely related: it is thermodynamics that connects them. Liu procedure is applied to analyze the thermodynamic requirements, and the comparison to the traditional method of divergence separation highlights the role of spacetime. It is shown that perfect Korteweg fluids are holographic. The co...

The motivation and research design for repeating the EPF experiments are described in the paper.

Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. The resulting field equation for the potential of this emergent force is nonline...

In a recent paper (V\'an, P.; Abe, S. Physica A 2022, 588, 126505), it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only gravitational and accordingly emergence of extended Newtonian gravity has been predicted. The resulting field equati...

The accuracy of the classical heat conduction model, known as Fourier's law, is highly questioned, dealing with the micro and nanosystems and biological tissues. In other words, the results obtained from the classical equations deviate from the available experimental data. It means that the continuum heat diffusion equation is insufficient and inap...

Torsion-balance measurements became well known in the early 1900s, with E\"otv\"os' famous high-precision verification of the equivalence of gravitational and inertial mass. This equivalence later became the basis of general relativity. A new chapter of these measurements began in 1985, when Fischbach and his colleagues discovered regularities in t...

The novel concept of spectral diffusivity is introduced to analyze the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is similar to mode analysis in wave propagation. The new modal quantities characterize dissipation and are best inter...

It is a long-lasting task to understand heat conduction phenomena beyond Fourier. Besides the low-temperature experiments on extremely pure crystals, it has turned out recently that heterogeneous materials with macro-scale size can also show thermal effects that cannot be modeled by the Fourier equation. This is called over-diffusive propagation, d...

Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s la...

The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is similar to mode analysis in wave propagation. The new modal quantities characterise dissipation and best interpret...

Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's la...

Limits of classical constitutive laws such as Fourier and Navier–Stokes equations are discovered since decades. However, the proper extensions—generalizations of these—are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely...

General constitutive equations of heat transport with second sound and ballistic propagation in isotropic materials are given using non-equilibrium thermodynamics with internal variables. The consequences of Onsager reciprocity relations between thermodynamic fluxes and forces and positive definiteness of the entropy production are considered. The...

The accuracy of the classical heat conduction model, known as Fourier's law, is highly questioned, dealing with the micro/nanosystems and biological tissues. In other words, the results obtained from the classical equations deviates from the available experimental data. It means that the continuum heat diffusion equation is insufficient and inappro...

It is a long-lasting task to understand heat conduction phenomena beyond Fourier. Besides the low-temperature experiments on extremely pure crystals, it has turned out recently that heterogeneous materials with macro-scale size can also show thermal effects that cannot be modelled by the Fourier equation. This is called over-diffusive propagation,...

A point charge is frequently approximated by various charge distributions deriving the Lorentz-Abraham-Dirac (LAD) equation. Here a rigid spherical shell is treated from this point of view. This particular continuum model is excellent to investigate whether some hidden expectations are true or not. It is shown here that the field of a uniformly cha...

The Einstein Telescope (ET) is a proposed next-generation, underground gravitational-wave detector to be based in Europe. It will provide about an order of magnitude sensitivity increase with respect to the currently operating detectors and, also extend the observation band targeting frequencies as low as 3 Hz. One of the first decisions that needs...

How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics? This ar...

The determination of deformation parameters of rock material is an essential part of any design in rock mechanics. The goal of this paper is to show, that there is a relationship between static and dynamic modulus of elasticity (E), modulus of rigidity (G) and bulk modulus (K). For this purpose, different data on igneous, sedimentary and metamorphi...

The Einstein Telescope (ET) is a proposed next-generation, underground gravitational-wave (GW) detector based in Europe. It will provide about an order of magnitude sensitivity increase with respect to currently operating detectors, and furthermore, extend the observation band towards lower frequencies, i.e., down to about 3\,Hz. One of the first d...

We show that the Hawking–Bekenstein entropy formula is modified by a factor of 8/3 if one also considers a work term in the 1st law of thermodynamics by a pressure stemming from the Hawking radiation. We give an intuitive definition for the corresponding thermodynamical volume by the implicit definition ϵ=Mc2/V, which is the average energy density...

There has been much interest in semiconductor superlattices because of their low thermal conductivities. This makes them especially suitable for applications in a variety of devices for the thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity...

The role of thermodynamics in continuum mechanics and the derivation of proper constitutive relations is a topic discussed in Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical of the heuristic methods of irreversible thermodynamics. In this paper, a small strain gradient elasti...

Regarding the entropy of charged and rotating Kerr-Newman black holes also as a function of the volume enclosed by the event horizon, $S=S(M,Q,J,V)$, we investigate the thermodynamic properties, in particular the stability problem of the system in standard four dimensions. By imposing the physical conditions of Euler homogeneity and a Stefan-Boltzm...

Being inspired by Verlinde's proposal that general relativistic gravity has a thermodynamic origin as an entropic force, Newtonian gravity is reexamined in view of nonequilibrium thermodynamics. Here, firstly, an unspecified scalar field potential is introduced and treated as a thermodynamic variable on an equal footing with the fluid variables. Th...

There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductiv...

Allen–CahnAllen–Cahn dynamics (Ginzburg–Landau) dynamicsGinzburg–Landau dynamics for scalar fields with heat conduction is treated in rigid bodies using a nonequilibrium thermodynamic framework with weakly nonlocal internal variablesInternal variableweakly nonlocal. The entropy production and entropy flux is calculated with the classical method of...

of the long term data taking, related to one of the proposed next generation ground-based gravitational detector’s location is presented here. Results of seismic and infrasound noise, electromagnetic attenuation and cosmic muon radiation measurements are reported in the underground Matra Gravitational and Geophysical Laboratory near Gyöngyösoroszi,...

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena...

The site characterisation of future underground gravitational wave detectors is based on spectral properties of the low frequency seismic noise. The evaluation of the collected long term seismological data in the Mátra Gravitational and Geophysical Laboratory revealed some aspects that are not apparent in short term spectral noise characterisation....

Classical gravitation is treated from the point of view of non-equilibrium thermodynamics. Gravitational potential is a thermodynamic state variable in a weakly nonlocal treatment. Entropy production is calculated and the simplest solution of the inequality with corresponding fluxes and forces is given. In case of ideal gravitation without dissipat...

Allen-Cahn (Ginzburg-Landau) dynamics for scalar fields with heat conduction is treated in rigid bodies using a non-equilibrium thermodynamic framework with weakly nonlocal internal variables. The entropy production and entropy flux is calculated with the classical method of irreversible thermodynamics by separating full divergences.

The general isotropic constitutive equations of heat conduction with second sound and ballistic propagation in isotropic materials is given using Non-Equilibrium Thermodynamics with Internal Variables (NET-IV). The consequences of Onsager reciprocity between thermodynamic fluxes and forces and positive definiteness of the entropy production is cons...

Limits of classical constitutive laws such as Fourier and Navier-Stokes equations are discovered since decades. However, the proper extensions - generalizations of these are not evident. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theory is discussed and compared to each other, namely...

of the long term data taking, related to one of the proposed next generation ground-based gravitational detector's location is presented here. Results of seismic and infrasound noise, electromagnetic attenuation and cosmic muon radiation measurements are reported in the underground Matra Gravitational and Geophysical Laboratory near Gy\"ongy\"osoro...

We derive two different generalized heat-transport equations: The most general one, of the first order in time and second order in space, encompasses some well known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe...

Dual phase lag equation for heat conduction is analyzed from the point of view of non-equilibrium thermodynamics. Its first order Taylor series expansion is consistent with the second law as long as the two relaxation times are not negative.

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs, and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier’s law for room-temperature phenomena in modeling of heterogen...

The selection of sites for underground gravitational wave detectors based on spectral and cumulative characterisation of the low frequency seismic noise. The evaluation of the collected long term seismological data in the M\'atra Gravitational and Geophysical Laboratory revealed several drawbacks of the previously established characteristics. Here...

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier's law for room temperature phenomena in modeling of heterogene...

The analysis of long term seismological data collected underground in the M\'atra Mountains, Hungary, using the facilities of the M\'atra Gravitational and Geophysical Laboratory (MGGL) is reported. The laboratory is situated inside the Gy\"ongy\"osoroszi mine, Hungary, 88m below the surface. This study focuses on the requirements of the Einstein T...

Assuming Euler homogeneity of the entropy we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. The homogeneity requires the usage of a volume in general relativity, for which various suggestions, scaling differently with the radius, are reviewed. Cons...

The Cahn-Hilliard and Ginzburg-Landau (Allen-Cahn) equations are derived from the second law. The intuitive approach by separation of full divergences is supported by a more rigorous method, based on Liu procedure and a constitutive entropy flux. Thermodynamic considerations eliminate the necessity of variational techniques and explain the role of...

The Cahn-Hilliard and Ginzburg-Landau (Allen-Cahn) equations are derived from the second law. The intuitive approach by separation of full divergences is supported by a more rigorous method, based on Liu procedure and a constitutive entropy flux. Thermodynamic considerations eliminate the necessity of variational techniques and explain the role of...

In this paper we present a thermodynamically consistent material model which is capable of modelling ductile-to brittle failure mode transition in ductile material undergoing deformations at high strain rates, and demonstrate the performance of the model in a numerical study using a fully coupled thermal-structural finite element analysis of a notc...

Second sound phenomenon and ballistic heat conduction, the two wave like propagation modes of heat, are the two most prominent, experimentally observed non-Fourier effects of heat conduction. In this paper we compare three related theories by quantitatively analyzing the crucial NaF experiments of Jackson, Walker and McNelly, where these effects we...

Matra Gravitational and Geophysical Laboratory (MGGL) has been established near Gy\"ongy\"osoroszi, Hungary in 2015, in the cavern system of an unused ore mine. The Laboratory is located at 88~m below the surface, with the aim to measure and analyse the advantages of the underground installation of third generation gravitational wave detectors. Spe...

▶ Describes the construction of advanced continuum theories ▶ Includes coupling between mechanical and thermal effects ▶ Helps readers obtain the necessary skills for creating new models using internal variables This book describes an effective method for modeling advanced materials like polymers, composite materials and biomaterials, which are,...

The overall description of thermomechanical processes inmicrostructured solids includes both direct and indirect couplings of equations of motion and heat conduction at the macrolevel. In addition to the conventional direct coupling, there exists the coupling between macromotion and microtemperature evolution. This means that the macrodeformation c...

It is demonstrated on the example of one-dimensional elastic pulse prop-agation that predictions of the Mindlin micromorphic theory may be inefficient if the size of inhomogeneity is comparable with the pulse length. This means that the Mindlin microelasticity is still an approximation of the description of the behavior of materials, which is satis...

The introduction of double dual internal variables provides the complete extension of the classical thermoelasticity theory onto the case of microstructured solids. This extension keeps the structure of canonical balances of momentum and energy and provides the thermodynamically consistent evolution equations for microdeformation and microtemperatu...

It is shown that inertial terms appear naturally in the thermodynamic theory with dual internal variables and the conditions of their appearance is well understandable in terms of mechanical notions. This demonstrates the difference between the standard single internal variable theory and the dual internal variables concept.

Several well-known dispersive wave propagation models together with generalization of the Mindlin-type models are derived by using internal variables. The adopted phenomenological approach is based on the material formulation of continuum mechanics and provides the full thermodynamic consistency due to the dual internal variables concept.

The introduction of nonlinear terms at both macro-and micro-levels does not change the formalism of the internal variable approach. In the non-dissipative case, the nonlinear terms can be balanced with dispersion providing the well-known models of solitonic behavior. The interplay between micro-and macro-nonlinearities allows to achieve more sophis...

Computations of thermoelasticwave propagation inmicrostructured solids show that besides the usual diffusion of the macrotemperature in course of time, the wave-type behavior of temperature is observed. This is possible because of coupling effects between microtemperature, stress, and macrotemperature. The reason why the microtemperature is governe...

The theory of a single internal variable of state is well established including the weak nonlocality and the enrichment by extra entropy flux. The theory is based on the consideration of the internal variable of state as a tool for taking into account the internal dissipation. Inertial effects are absent in this theory by definition, which leads to...

It is demonstrated that the dual internal variable approach is able to predict a hyperbolic character of heat conduction at the microscale. One of the internal variables is identified with microtemperature, i.e., the fluctuation of macroscopic temperature due to the inhomogeneity of the body. The macroscopic heat conduction equation remains parabol...

Wave dispersion is a characteristic feature of solids with microstructure. The development of models of linear wave dispersion effects in isotropic solids is used as an example of the construction of more and more sophisticated dispersive wave equations. The considered models are distinct in foundations and derivations.

It is shown how dual weakly non-local internal variables and extra entropy fluxes can be introduced in the framework of canonical thermomechanics on the material manifold. This extension of the single internal variable formalism allows one to derive a hyperbolic evolution equation for internal variables in the non-dissipative case. Since the dissip...

Two-dimensional simulations of the heat pulse propagation experiment show that there exists an influence of the internal substructure of the material on the results. This influence is significant and unavoidable. Numerical simulations confirm that prediction of temperature behavior at the rear surface of the sample by the Fourier law are systematic...

The conditions of existence of extra mass flux in single component dissipative non-relativistic fluids are clarified. By considering Galilean invariance we show that if total mass flux is equal to total momentum density, then mass, momentum, angular momentum and booster (center- of-mass) are conserved. However, these conservation laws may be fulfil...

Galilean transformation properties of different physical quantities are investigated from the point of view of four dimensional Galilean relativistic (non-relativistic) space-time. The objectivity of balance equations of general heat conducting fluids and of the related physical quantities is treated as an application.

Heat conduction at low temperatures show various effects that cannot be described by the Fourier law, like the second sound and ballistic propagation. In this paper the performance of various theories is compared in case of ballistic and wave like propagation of heat pulses in NaF.

A Mátrai Gravitációs és Geofi zikai Laboratórium (MGGL) a rekultiváció alatt álló gyöngyösoroszi mélyművelésű bányában épült 2015-ben. A 88 m-rel a földfelszín alatt található létesítményben a harmadik generációs gravitációshullám-detektorok föld alatti telepítésének és folyamatos működésének lehetőségét vizsgáljuk. Szeizmikus, infrahang- és elektr...

Single component Galilean-relativistic (nonrelativistic) fluids are treated independently of reference frames. The basic fields are given, their balances, thermodynamic relations and the entropy production is calculated. The usual relative basic fields, the mass, momentum and energy densities, the diffusion current density, the pressure tensor and...

We report heat pulse experiments at room temperature that cannot be described by Fourier's law. The experimental data is modelled properly by the Guyer--Krumhansl equation, in its over-diffusion regime. The phenomenon is due to conduction channels with differing conductivities, and parallel to the direction of the heat flux.

The origin of microinertia of micromorphic theories is investigated from the point of view of non-equilibrium thermodynamics. In the framework of dual internal variables microinertia stems from a thermodynamic equation of state related to the internal variable with the properties of mechanical momentum.

A novel equation of heat conduction is derived with the help of a generalized entropy current and internal variables. The obtained system of constitutive relations is compatible with the momentum series expansion of the kinetic theory. The well known Fourier, Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys-type, and Cahn-Hilliard type equation...

Rate- and state-dependent friction law for velocity-step and healing are analysed from a thermodynamic point of view. Assuming a logarithmic deviation from steady-state a unification of the classical Dieterich and Ruina models of rock friction is proposed.

The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments.

Non-equilibrium thermodynamics with internal variables introduces a natural hierarchical arrangement of evolution equations. Three examples are shown: a hierarchy of linear constitutive equations in thermodynamic rhelogy with a single internal variable, a hierarchy of wave equations in the theory of generalized continua with dual internal variables...

Prediction of the thermoelastic behavior of microstructured materials suggests a more general description of thermal processes in addition to the generalized continuum description extending the conventional continuum mechanics for incorporating intrinsic microstructural effects. Double dual internal variables are introduced in order to couple inert...

Postulating a particular quantum correction to the source term in the classical Einstein equation we identify the conformal content of the above action and obtain classical gravitation for massive particles, but with a cosmological term representing off-mass-shell contribution to the energy-momentum tensor.