Péter Ván

Internal Variables and Dynamic Degrees of Freedom

Abstract Dynamic degrees of freedom and internal variables are treated in a uniform way. The unification is achieved by means of the introduction of a dual internal variable. This duality provides the corresponding evolution equations depending on whether the Onsager–Casimir reciprocity relations are satisfied or not.

Weakly nonlocal irreversible thermodynamics

Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.

Universality in heat conduction theory: Weakly nonlocal thermodynamics

A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current intensity factor. A general constitutive evolution equation of the current density of the internal energy is derived by introducing linear relationship between the thermodynamic forces and fluxes. The Fourier, Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type and Green-Naghdi type equations of heat conduction are obtained as special cases. The universal character of the approach is demonstrated by two examples. Solutions illustrating the properties of the equation with jump boundary conditions are given.

Zeroth law compatibility of nonadditive thermodynamics

Nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules [corrected]. In this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics. We find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these. Our result offers a possible solution to the long-standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters.

Quark-gluon plasma connected to finite heat bath

We derive Tsallis entropy, Sq, from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result for finite thermostats interprets thermodynamically the subsystem temperature, T1, and the index q in terms of the temperature, T, entropy, S, and heat capacity, C of the reservoir as T1 = T exp(-S/C) and q = 1 - 1/C. In the infinite C limit, irrespective to the value of S, the Boltzmann-Gibbs approach is fully recovered. We apply this framework for the experimental determination of the original temperature of a finite thermostat, T, from the analysis of hadron spectra produced in high energy collisions, by analyzing frequently considered simple models of the quark-gluon plasma.

RELATIVISTIC HYDRODYNAMICS - CAUSALITY AND STABILITY

Abstract.Causality and stability in relativistic dissipative hydrodynamics are important conceptual issues. We argue that causality is not restricted to hyperbolic set of differential equations. E.g. heat conduction equation can be causal considering the physical validity of the theory. Furthermore we propose a new concept of relativistic internal energy that clearly separates the dissipative and non-dissipative effects. We prove that with this choice we remove all known instabilities of the linear response approximation of viscous and heat conducting relativistic fluids. In this paper the Eckart choice of the velocity field is applied.

First order and stable relativistic dissipative hydrodynamics

Abstract Relativistic thermodynamics is derived from kinetic equilibrium in a general frame. Based on a novel interpretation of Lagrange multipliers in the equilibrium state we obtain a generic stable but first order relativistic dissipative hydrodynamics. Although this was believed to be impossible, we circumvent this difficulty by a specific handling of the heat flow.

The effects of nonlocality on the evolution of higher order fluxes in nonequilibrium thermodynamics

The role of gradient dependent constitutive spaces is investigated on the example of Extended Thermodynamics of rigid heat conductors. Different levels of nonlocality are developed and the different versions of extended thermodynamics are classified. The local form of the entropy density plays a crucial role in the investigations. The entropy inequality is solved under suitable constitutive assumptions. Balance form of evolution equations is obtained in special cases. Closure relations are derived on a phenomenological level.

Weakly nonlocal irreversible thermodynamics—the Guyer–Krumhansl and the Cahn–Hilliard equations

Abstract Examples of irreversible thermodynamic theory of nonlocal phenomena are given, based on generalized entropy current. Thermodynamic currents and forces are identified to derive the Guyer–Krumhansl and Cahn–Hilliard equations. In the latter case Gurtins rate dependent additional term is received through the thermodynamic approach.

Deviation from the Fourier law in room-temperature heat pulse experiments

Abstract We report heat pulse experiments at room temperature that cannot be described by Fouriers law. The experimental data are modeled properly by the Guyer–Krumhansl equation, in its over-diffusion regime. The phenomenon may be due to conduction channels with differing conductivities and parallel to the direction of the heat flux.