Giorgio V. Sonnino

Nonlinear closure relations theory for transport processes in nonequilibrium systems.

Abstract A new formulation of the thermodynamic field theory (TFT) is presented. In this new version, one of the basic restriction in the old theory, namely a closed-form solution for the thermodynamic field strength, has been removed. In addition, the general covariance principle is replaced by Prigogine’s thermodynamic covariance principle (TCP). The introduction of TCP required the application of an appropriate mathematical formalism, which has been referred to as the isoentropic formalism. The validity of the Glansdorff-Prigogine Universal Criterion of Evolution, via geometrical arguments, is proven. A new set of thermodynamic field equations, able to determine the nonlinear corrections to the linear (”Onsager”) transport coefficients, is also derived. The geometry of the thermodynamic space is non-Riemannian tending to be Riemannian for hight values of the entropy production. In this limit, we obtain again the same thermodynamic field equations found by the old theory. Applications of the theory, such as transport in magnetically confined plasmas, materials submitted to temperature and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein.

Comment on "Maximum or minimum entropy production? How to select a necessary criterion of stability for a dissipative fluid or plasma".

In a recent paper, Phys. Rev. E 81, 041137 (2010), the author attempts to derive ten necessary conditions for the stability of dissipative fluids and plasmas. Assuming the validity of the local equilibrium principle, these criteria have been obtained solely from the first and second laws of thermodynamics. The Onsager reciprocity relations have not been invoked, and the authors results are supposed to be valid independent of the choice of the boundary conditions. In the present Comment, in agreement with the general theory established by Glansdorff-Prigogine in 1954 and 1970, we show that there is no variational principle expressing the necessary conditions for the stability of dissipative systems involving convective effects when the system is out of the Onsager region. In particular, we prove that the basic equations constituting the starting point of the analysis of the author, attempting to derive ten necessary conditions for the stability involving magnetohydrodynamical effects, are incorrect and in contradiction with the laws of the thermodynamics of irreversible processes.

Nonlinear transport processes in tokamak plasmas. I. The collisional regimes

An application of the thermodynamic field theory (TFT) to transport processes in L-mode tokamak plasmas is presented. The nonlinear corrections to the linear (“Onsager”) transport coefficients in the collisional regimes are derived. A quite encouraging result is the appearance of an asymmetry between the Pfirsch–Schluter (P-S) ion and electron transport coefficients: the latter presents a nonlinear correction, which is absent for the ions, and makes the radial electron coefficients much larger than the former. Explicit calculations and comparisons between the neoclassical results and the TFT predictions for Joint European Torus (JET) plasmas are also reported. It is found that the nonlinear electron P-S transport coefficients exceed the values provided by neoclassical theory by a factor that may be of the order 102. The nonlinear classical coefficients exceed the neoclassical ones by a factor that may be of order 2. For JET, the discrepancy between experimental and theoretical results for the electron los...

Geometrical thermodynamic field theory

A manifestly covariant, coordinate independent reformulation of the thermodynamic field theory (TFT) is presented. The TFT is a covariant field theory that describes the evolution of a thermodynamic system, extending the near-equilibrium theory established by Prigogine in 1954. We introduce the minimum rate of dissipation principle, which applies to any system relaxing toward a steady state. We also derive the thermodynamic field equations, which in the case of α–α and β–β processes have already appeared in the literature. In more general cases, the equations are notably simpler than those previously encountered, and they extend beyond the weak-field regime. Finally, we derive the equations that determine the steady states as well as the critical values of the control parameters beyond which a steady state becomes unstable.

Thermodynamic Field Theory (An Approach to Thermodynamics of Irreversible Processes)

The thermodynamic field theory (TFT) allows to deal with thermodynamic systems submitted even to strong non-equilibrium conditions. The theory herein formulated enables to find field equations whose solutions give the generalised relations between the thermodynamic forces and their conjugated flows. It will be shown that evolution of the thermodynamic systems is well described in the Weyl’s space. In the particular case in which the thermodynamic forces and conjugated flows are linked only through a symmetric tensor (the metric tensor), the resulting geometry is the Riemannian geometry. As example of application, the thermoelectric effect and the unimolecular triangular chemical reaction are analysed in great detail.

Self-Replicating Spots in the Brusselator Model and Extreme Events in the One-Dimensional Case with Delay

We consider the paradigmatic Brusselator model for the study of dissipative structures in far from equilibrium systems. In two dimensions, we show the occurrence of a self-replication phenomenon leading to the fragmentation of a single localized spot into four daughter spots. This instability affects the new spots and leads to splitting behavior until the system reaches a hexagonal stationary pattern. This phenomenon occurs in the absence of delay feedback. In addition, we incorporate a time-delayed feedback loop in the Brusselator model. In one dimension, we show that the delay feedback induces extreme events in a chemical reaction diffusion system. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical distribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback intensity. The generality of our analysis suggests that the feedback-induced instability leading to the spontaneous formation of rogue waves in a controllable way is a universal phenomenon.

Free convection experiments in water and deuterated mixtures at temperatures including the density maxima

Abstract An apparatus designed to perform free convection experiments in cylindrical liquid samples under strictly controlled boundary conditions is described. Convection experiments are carried out by measuring at the centre of the sample temperature vs time, as monitored by a thermocouple and a computer on-line device. The system water-deuterated water has been investigated in temperature ranges including the density maxima of the samples and compared, only in the case of pure water, with theory. Previously observed anomalies of the convective behaviour in this range are confirmed in the form of typical ‘plateaux’ and thoroughly examined to provide new information about the density maximum of isotopic mixtures. A new effect of a faster cooling appears, near the maximum density, when the boundary temperature is brusquely increased.

Long-Ranged Correlations in Bounded Nonequilibrium Fluids

In a recent paper, Liu and Oppenheim [J. Stat. Phys.86:179 (1997)] solve the fluctuating heat diffusion equation for a bounded system with a temperature gradient. This note demonstrates that, contrary to their claims, their solution for the temperature correlation function is indeed long-ranged and reduces to that of Garcia et al.[J. Stat. Phys.47:209 (1987)].

Non-linear, unsteady free convection in a vertical cylinder submitted to a horizontal thermal gradient: measurements in water between 6 and 21°C and a theoretical model of convection

Abstract The non-linear, unsteady behaviour of water contained in a vertical cylinder of yellow brass when submitted to a horizontal initial thermal gradient is investigated by following the temperature decay in the centre of a cylinder. Experimental results are interpreted by means of a theoretical model which allows the deduction of equations for temperature, velocity, pressure and density in the nucleus. The new equations are compared with those of conduction to provide an evaluation of the convective contribution to heat transfer. Our data indicate that when a characteristic dimensionless group which has the form of a Rayleigh number reaches a critical value of 1600 ± 50, the heat transfer may be described by a pure conduction equation.

Symmetry group and group representations associated with the thermodynamic covariance principle

The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e., the flux-force relations) valid for thermodynamic systems out of Onsagers region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e., under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noethers theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed.