arXiv subjects

Alberto Sonnino

Publications and source records attributed to Alberto Sonnino.

62 records · Page 4Linked to original sources

arXiv2015

The Thermodynamic Covariance Principle

The concept of {\it equivalent systems} from the thermodynamic point of view, originally introduced by Th. De Donder and I. Prigogine, is deeply investigated and revised. From our point of view, two systems are thermodynamically equivalent if, under transformation of the thermodynamic forces, both the entropy production and the Glansdorff-Prigogine dissipative quantity remain unaltered. This kind of transformations may be referred to as the {\it Thermodynamic Coordinate Transformations} (TCT). The general class of transformations satisfying the TCT is determined. We shall see that, also in the nonlinear region ({\it i.e.}, out of the Onsager region), the TCT preserve the reciprocity relations of the transformed transport matrix. The equivalent character of two transformations under TCT, leads to the concept of {\it Thermodynamic Covariance Principle} (TCP) stating that all thermodynamic equations involving the thermodynamic forces and flows ({\it e.g.}, the closure flux-force relations) should be covariant under TCT.

physics.class-ph↗

arXiv2015

Minimum Dissipation Principle in Nonlinear Transport

We extend Onsager's minimum dissipation principle to stationary states that are only subject to local equilibrium constraints, even when the transport coefficients depend on the thermodynamic forces. Crucial to this generalization is a decomposition of the thermodynamic forces into those that are held fixed by the boundary conditions, and the subspace which is orthogonal with respect to the metric defined by the transport coefficients. We are then able to apply Onsager and Machlup's proof to the second set of forces. As an example we consider two-dimensional nonlinear diffusion coupled to two reservoirs at different temperatures. Our extension differs from that of Bertini et al. in that we assume microscopic irreversibility and we allow a nonlinear dependence of the fluxes on the forces.

cond-mat.stat-mech↗

arXiv2014

Stationary distribution functions for Tokamak-plasmas in the weak-collisional transport regime by MaxEnt principle

In previous works, we derived stationary density distribution functions (DDF) where the local equilibrium is determined by imposing the maximum entropy (MaxEnt) principle, under the scale invariance restrictions, and the minimum entropy production theorem. In this paper we demonstrate that it is possible to reobtain these DDF solely from the MaxEnt principle subject to suitable scale invariant restrictions in all the variables. For the sake of concreteness, we analyze the example of ohmic, fully ionized, tokamak-plasmas, in the weak-collisional transport regime. In this case we show that it is possible to reinterpret the stationary distribution function in terms of the Prigogine distribution function where the logarithm of the DDF is directly linked to the entropy production of the plasma. This leads to the suggestive idea that also the stationary neoclassical distribution functions, for magnetically confined plasmas in the collisional transport regimes, may be derived solely by the MaxEnt principle.

cond-mat.stat-mech↗

arXiv2014

The Rényi entropy of Lévy distribution

The equivalence between non-extensive C. Tsallis entropy and the extensive entropy introduced by Alfréd Rényi is discussed. The Rényi entropy is studied from the perspective of the geometry of the Lebesgue and generalised, exotic Lebesgue spaces. A duality principle is established. The Rényi entropy for the Lévy distribution, in the domain when the nunerical methods fails, is approximated by asymptotic expansion for the large values of the Rényi parameter.

physics.data-an↗

arXiv2013

Reference Distribution Functions for Magnetically Confined Plasmas from the Minimum Entropy Production Theorem and the MaxEnt Principle, subject to the Scale-Invariant Restrictions

We derive the expression of the reference distribution function for magnetically confined plasmas far from the thermodynamic equilibrium. The local equilibrium state is fixed by imposing the minimum entropy production theorem and the maximum entropy (MaxEnt) principle, subject to scale invariance restrictions. After a short time, the plasma reaches a state close to the local equilibrium. This state is referred to as the reference state. The aim of this letter is to determine the reference distribution function (RDF) when the local equilibrium state is defined by the above mentioned principles. We prove that the RDF is the stationary solution of a generic family of stochastic processes corresponding to an universal Landau-type equation with white parametric noise. As an example of application, we consider a simple, fully ionized, magnetically confined plasmas, with auxiliary Ohmic heating. The free parameters are linked to the transport coefficients of the magnetically confined plasmas, by the kinetic theory.

cond-mat.stat-mech↗

arXiv2013

Derivation of Reference Distribution Functions for Tokamak-plasmas by Statistical Thermodynamics

A general approach for deriving the expression of reference distribution functions by statistical thermodynamics is illustrated, and applied to the case of a magnetically confined plasma. The local equilibrium is defined by imposing the minimum entropy production, which applies only to the linear regime near a stationary thermodynamically non-equilibrium state and the maximum entropy principle under the scale invariance restrictions. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces, however, for concreteness, we analyze, afterwords, a magnetically confined plasma subject to three thermodynamic forces, and three energy sources: i) the total Ohmic heat, supplied by the transformer coil, ii) the energy supplied by Neutral Beam Injection (NBI), and iii) the RF energy supplied by Ion Cyclotron Resonant Heating (ICRH) system which heats the minority population. In this limit case, we show that the derived expression of the distribution function is more general than that one, which is currently used for fitting the numerical steady-state solutions obtained by simulating the plasma by gyro-kinetic codes. An application to a simple model of fully ionized plasmas submitted to an external source is discussed. Through kinetic theory, we fixed the values of the free parameters linking them with the external power supplies. The singularity at low energy in the proposed distribution function is related to the intermittency in the turbulent plasma.

cond-mat.stat-mech↗

arXiv2013

Family of Probability Distributions Derived from Maximal Entropy Principle with Scale Invariant Restrictions

Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, whose stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.

cond-mat.stat-mech↗

arXiv2012

Rotation of Tokamak-Plasmas out of Mechanical Equilibria, in Absence of External Torques

Rotation of tokamak-plasmas, not at the mechanical equilibrium, is investigated utilizing a theorem of thermodynamics, established by Prigogine. This theorem, suitably applied to toroidally confined plasmas, suggests that the global barycentric rotations of the plasma, in the toroidal and poloidal directions, are pure reversible processes. In case of negligible viscosity and by supposing the validity of the balance equation for the internal forces, we show that the plasma, even not in the mechanical equilibrium, may freely rotate as a rigid body in the toroidal direction with an angular frequency with an angular frequency, which may be higher than the neoclassical estimation. In addition, its toroidal rotation may cause the plasma to rotate globally in the poloidal direction at a speed faster than the expression found by the neoclassical theory. The eventual configuration is attained when the toroidal and poloidal angular frequencies reaches the values that minimize dissipation.

physics.plasm-ph↗