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Peter Ván

Publications and source records attributed to Peter Ván.

15 recordsLinked to original sources
arXiv2026

Constitutive Modelling of Korteweg Fluids Using Liu's Method

The paper studies constitutive modelling of Korteweg fluids. Thermodynamic consistency, i.e. compatibility with entropy balance law, is achieved using Liu's method of multipliers. Appropriate constitutive assumptions facilitated inclusion of the capillary effects in the specific entropy. Korteweg stresses are derived from the equilibrium conditions -- vanishing of the entropy production and its minimization in equilibrium. Material parameter in Korteweg stresses is allowed to depend on temperature, which turns out to be consistent with kinetic-theory results and leads to cross-coupling of mechanical and thermal effects. The generalized Gibbs' relation, which inherits the capillary effects, is derived as consequence, which is a peculiar feature of the Liu's method.

physics.flu-dyn↗
arXiv2026

Thermodynamic conditions ensure the stability of third-order extended heat conduction

In a recent work, Somogyfoki et al. (J. Non-Equilib. Thermodyn. 50, 59-76, 2025) analysed the linear stability of homogeneous equilibrium in third-order non-Fourier heat conduction within the framework of non-equilibrium thermodynamics with internal variables. They identified a stability condition, their equation (49), which could not be derived from the standard thermodynamic inequalities for the 2X2 conductivity blocks, and concluded that the Second Law does not guarantee stability in the most general case. Here we show that this conclusion was due to an overly conservative proof strategy: the standard thermodynamic conditions (concave entropy and non-negative entropy production, as expressed by the $2\times2$ block positive-definiteness inequalities (19)-(20) of the original paper) do suffice for linear stability. The key observation is that all coefficients of the dispersion polynomial remain positive for all physical wave numbers because their structure prevents positive real roots. This result confirms that thermodynamics, understood as a stability theory, ensures fundamental dynamic stability in all thermodynamically consistent third-order extended heat conduction theories. A comparison with the rate-equation approach of Giorgi, Morro and Zullo (Meccanica 59, 1757-1776, 2024) is also presented.

cond-mat.stat-mech↗
arXiv2026

About the dissipative Newton equation

The thermodynamic basis of classical mechanics is presented. In this framework, ideal Newtonian mechanics emerges as the zero-dissipation limit of a more general, dissipative theory. The thermodynamic approach predicts a novel dissipative contribution to the momentum that depends on the applied force, leading to a damping coefficient with a specific, experimentally testable dependence on the inertial mass and the spring constant. A torsion balance experiment with variable moment of inertia has been designed to measure this effect. Several known equations, including a thermodynamic version of the Eliezer-Ford-O'Connell equation of radiation reaction, are recovered as special cases.

physics.class-ph↗
arXiv2025

Some remarks on the objectivity and thermodynamic consistency of Korteweg-type fluids

In this note we compare the entropy principle and the objectivity arguments in the methodologies of Dunn and Serrin [1] and in the more recent weakly nonlocal thermodynamic analysis of Korteweg-type fluids in [2]. It is concluded that the different objectivity approaches lead to the same constitutive functions, and that the difference in the thermodynamically compatible pressure tensors of perfect Korteweg fluids is due to different symmetry requirements.

cond-mat.stat-mech↗
arXiv2023

Holographic fluids: a thermodynamic road to quantum physics

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 holographic. The conditions under which a complex field can represent the density and velocity fields of the fluid, and where the complex scalar field becomes a wave function of quantum mechanics, are explored. The bridge between the field and particle representations of a physical system is holography, and the key to holography is the Second Law of thermodynamics.

physics.flu-dyn↗
arXiv2023

Toward a Universal Theory of Stable Evolution

The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and stable ones survive. The physical concepts from the stability structure and the related formalism of constrained entropy inequality are universal by construction. Therefore, the mathematical tools and the physical concepts of thermodynamics help formulate dynamical theories of any systems in social and natural sciences.

physics.soc-ph↗
arXiv2022

Crossover in extended Newtonian gravity emerging from thermodynamics

In a recent paper (Ván, 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 equation for the potential of this emergent force is nonlinear and admits the logarithmic potential as a singular solution, suggesting its relevance to the dark matter conundrum. Here, a general analysis of the nonlinear field equation is performed. It is found that the emergent force field exhibits the unsharp crossover between the 1/r and 1/r^2 forces outside the fluid, depending on a spatial scale characteristic of the present theory to be observationally tested in the context of the dark matter conundrum. Then, the action functional is constructed for the potential of the emergent field and the field energy is shown to be free from an infrared divergence. A comment is also made on the difference of the present theory from MOND (modified Newtonian dynamics).

astro-ph.GA↗
arXiv2022

Lagging Heat Models in Thermodynamics and Bioheat Transfer: a Critical Review

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 inappropriate for modeling heat transport in these cases. There are several techniques for modeling non-Fourier heat conduction. In the present paper, we place our focus on the dual-phase-lag (DPL) approach. The DPL model, as a popular modification of Fourier's law, has already been utilized in numerous situations, such as simulating ultrafast laser heating and heat conduction in carbon nanotubes. There has been a sharp increase in research on non-Fourier heat conduction in recent years. Several studies have been performed in the fields of thermoelasticity, thermodynamics, transistor modeling, and bioheat transport. This review presents the most recent non-Fourier bioheat conduction works and the related thermodynamics background. The various mathematical tools, modeling different thermal therapies, and relevant criticisms and disputes are discussed. Finally, the novel and other possible studies are also presented to provide a better overview, and the roadmap to the future research and challenges ahead is drawn up.

physics.app-ph↗
arXiv2021

Emergence of extended Newtonian gravity from thermodynamics

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 constraint on the field, and, quite remarkably, the allowable field turns out to be only of gravity. The resulting field equation for the gravitational potential derived from the analysis of the entropy production rate contains a dissipative term due to irreversibility. It is found that the system relaxes to the conventional theory of Newtonian gravity up to a certain spatial scale, whereas on the larger scale there emerges non-Newtonian gravity described by a nonlinear field equation containing a single coefficient. A comment is made on an estimation of the coefficient that has its origin in the thermodynamic property of the system.

cond-mat.stat-mech↗
arXiv2021

Spectral properties of dissipation

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 interpreted as effective diffusivities, or, in case of heat conduction, as effective heat conductivities of the material.

physics.class-ph↗
arXiv2020

Thermodynamically consistent gradient elasticity with an internal variable

The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical with the heuristic methods of irreversible thermodynamics. In this paper, a small strain gradient elasticity theory is constructed with memory effects and dissipation. The method is nonequilibrium thermodynamics with internal variables; therefore, the constitutive relations are compatible with thermodynamics by construction. Thermostatic Gibbs relation is introduced for elastic bodies with a single tensorial internal variable. The thermodynamic potentials are first-order weakly nonlocal, and the entropy production is calculated. Then the constitutive functions and the evolution equation of the internal variable is constructed. The second law analysis has shown a contribution of gradient terms to the stress, also without dissipation.

cond-mat.stat-mech↗
arXiv2017

Weakly nonlocal nonequilibrium thermodynamics: the Cahn-Hilliard equation

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 functional derivatives.

cond-mat.stat-mech↗
arXiv2016

Extra mass flux in fluid mechanics

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 fulfilled also by other means. We show an example of weakly non-local hydrodynamics where the conservation laws are satisfied as well although the total mass flux is different from momentum density.

physics.flu-dyn↗