A steady-state system in non-equilibrium thermodynamics including thermal and electrical effects

The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet–Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

On the evolution of higher order fluxes in non-equilibrium thermodynamics

The connection between the balance structure of the evolution equations of higher order fluxes and different forms of the entropy current is investigated using the example of rigid heat conductors. Compatibility conditions of the theories are given. Thermodynamic closure relations are derived.     

The prefactor of the stationary probability distribution in variational non-equilibrium thermodynamics

According to the Kubo Approximation in the large volume asymptotic, the stationary distribution probability of a Master equation can be approximated as U₀(x)exp(−VΦ). Here V is the volume, Φ is the information potential which generalizes the free energy to non-equilibrium situation and U₀ is a prefactor obtained by solving a first order partial differential equation. In this article, we study the properties of U₀ and prove that it can be obtained by integration along the trajectories of a certain vector field. We also show that these trajectories cannot be chaotic. This is necessary in order to insure that the Kubo approximation is valid.     

Non-extensive thermodynamics and stationary processes of localization

We focus our attention on dynamical processes characterized by an entropic index Q<1. According to the probabilistic arguments of Tsallis, C and Bukman, DJ [Phys Rev E 1996;54:R2197] these processes are subdiffusional in nature. The non-extensive generalization of the Kolmogorov–Sinai (KS) entropy yielding the same entropic index implies the stationary condition. We note, on the other hand, that enforcing the stationary property on subdiffusion has the effect of producing a localization process occurring within a finite time scale. We thus conclude that the stationary dynamic processes with Q<1 must undergo a localization process occurring at a finite time. We check the validity of this conclusion by means of a numerical treatment of the dynamics of the logistic map at the critical point.     

Nonequilibrium statistical thermodynamics of cascade processes in solids: the quasi temperature of cascade particles

Displacement cascades in solids are investigated in the framework of nonequilibrium statistical thermodynamics. The quasi temperature of a subsystem of cascade particles in metals and semiconductors is derived using the energy balance equation for a cascade process.     

Thermodynamic potentials for non-equilibrium systems

The notion of non-equilibrium potential for systems far from equilibrium is reviewed and the relation to the reversed process is examined. The potential is constructed in the neighborhood of the homogeneous attractors for a non-variational extended system, namely the subcritical complex Ginzburg–Landau equation. This construction is the second known example of a Lyapunov functional for a non-variational system.     

Supercritical mesoscopic thermodynamics

In this paper, a new approach to the two-body problem is considered in greater detail than in previous papers of the author. The semiclassical transition from quantum statistics to classical statistics is studied and an analog of superfluidity in classical thermodynamics for supercritical states is obtained.     

On thermodynamics and intrinsically equilibrated materials

Summary The existence and uniqueness of free energy functions is demonstrated for a class of materials broad enough to contain as special cases those of the theory of finite elasticity, the theory of hypo-elasticity, and the theory of internal state variables for which the path of evolution is invariant under rescalings of time. Dedicated toDario Graffi on his 70th Birthday Entrata in Redazione il 24 giugno 1975. This research was supported by the U. S. National Science Foundation under Grant GP-32951X2.     

Mechanics of deformed media and thermodynamics

The application of thermodynamics to the mechanics of deformed media is reviewed. The thermodynamic methods were found to be especially effective in studying creep strains, laws of limiting stress, and other phenomena in polymeric materials. The review encompasses the most important studies in this field published mainly during the past five years.     

Transport properties of non-equilibrium ionized argon gas

Zusammenfassung Die Arbeit behandelt das Verhalten eines teilweise ionisierten Gases in einem elektrischen Feld sowie die experimentalle Bestimmung von Transporteigenschaften, beruhend auf einer modifizierten Grenzschichttheorie und Messungen in einer zweidimensionalen Kanalströmung.

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Study supported by National Science Foundation under grant No. G-19 926.     

Ergodicity of non-equilibrium Glauber dynamics in continuum

We study asymptotic properties of the continuous Glauber dynamics with unbounded death and constant birth rates. In particular, an information about the location of the spectrum for the symbol of the Markov generator is obtained. The latter fact is used for the proof of the ergodicity of this process. We show that the speed of convergence to the equilibrium is exponential.     

Microscopic rheological models and extended irreversible thermodynamics

The expressions of the constitutive equations of dilute polymer solutions, as predicted by the main microscopic rheological models, are shown to be in agreement with these derived from extended irreversible thermodynamics. Accord between the thermodynamic and Boltzmann microscopic expressions of entropy is also completed for steady state flows.     

Tunnel quantization of thermodynamics and critical exponents

Mathematical Notes - In the paper, it is shown that the critical indices of practical simple liquids, as well as many other thermodynamical effects, readily and naturally follow from the conception...