Thermodynamics, of irreversible processes

Let us now provide a brief summary of the application of the thermodynamics of irreversible processes to diffusion [6,12,21,22], 

In an irreversible process, in conformity with the second law of thermodynamics, the magnitude that determines the time dependence of an isolated thermodynamic system is the entropy, S [23-26], Consequently, in a closed system, processes that merely lead to an increase in entropy are feasible. The necessary and sufficient condition for a stable state, in an isolated system, is that the entropy has attained its maximum value [26], Therefore, the most probable state is that in which the entropy is maximum. 

Irreversible processes are driven by generalized forces, X, and are characterized by transport (or Onsager) phenomenological coefficients, L [21,22], where these transport coefficients, Lip are defined by linear relations between the generalized flux densities,./, which are the rates of change with time of state variables, and the corresponding generalized forces X . 

Familiar examples of the relation between generalized fluxes and forces are Fick s first law of diffusion, Fourier s law of heat transfer, Ohm s law of electricity conduction, and Newton s law of momentum transfer in a viscous flow. 

In the realm of the previously stated principles, the real driving force behind mass transport is the gradient of chemical potential in this sense, in the absence of an external Newtonian force like that exerted in a charged species by an electric field, it is expressed as 

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L. Onsager (Yale) discovery of the reciprocity relations bearing his name, which are fundamental for the thermodynamics of irreversible processes. 

Thermodynamics of Irreversible Processes Applications to Diffusion and Rheology... 

R. Haase, Thermodynamics of irreversible processes, Dover Publications, Mineola (NY), 1990. 

If Onsager s great achievement with the thermodynamics of irreversible processes met with initial indifference, Onsager s next feat created a sensation ill the scientific world. In a discussion remark in 1942, he disclosed that he had solved exactly the two-dimensional Ismg model, a model of a ferro-magnet, and showed that it had a phase transition with a specific heat that rose to infinity at the transi-... 

Prigogine, I. Introduction to Thermodynamic of Irreversible Processes, 2nd ed, New York, Wiley 1961... 

There are three different approaches to a thermodynamic theory of continuum that can be distinguished. These approaches differ from each other by the fundamental postulates on which the theory is based. All of them are characterized by the same fundamental requirement that the results should be obtained without having recourse to statistical or kinetic theories. None of these approaches is concerned with the atomic structure of the material. Therefore, they represent a pure phenomenological approach. The principal postulates of the first approach, usually called the classical thermodynamics of irreversible processes, are documented. The principle of local state is assumed to be valid. The equation of entropy balance is assumed to involve a term expressing the entropy production which can be represented as a sum of products of fluxes and forces. This term is zero for a state of equilibrium and positive for an irreversible process. The fluxes are function of forces, not necessarily linear. However, the reciprocity relations concern only coefficients of the linear terms of the series expansions. Using methods of this approach, a thermodynamic description of elastic, rheologic and plastic materials was obtained. 

Prigogine, 1. (1967). "Introduction to Thermodynamics of Irreversible Processes." Wiley-Interscience, New York. 

Haase, R. Thermodynamics of Irreversible Processes Dover New York, 1969. 

KuUcen, GDC, Thermodynamics of Irreversible Processes WUey Chichester, UK, 1994. Landau, LD Lifshitz, EM Pitaevsldi, LP, Electrodynamics of Continuous Media, 2nd ed. Pergamon Press Oxford, 1984. 

Prigogine, I., Introduction to Thermodynamics of Irreversible Processes, John Wiley Sons, New York, 1967. 

Some of the elements of thermodynamics of irreversible processes were described in Sections 2.1 and 2.3. Consider the system represented by n fluxes of thermodynamic quantities and n driving forces it follows from Eqs (2.1.3) and (2.1.4) that n(n +1) independent experiments are needed for determination of all phenomenological coefficients (e.g. by gradual elimination of all the driving forces except one, by gradual elimination of all the fluxes except one, etc.). Suitable selection of the driving forces restricted by relationship (2.3.4) leads to considerable simplification in the determination of the phenomenological coefficients and thus to a complete description of the transport process. 

Equilibrium thermodynamics was developed about 150 years ago. It is concerned only with the achievement of an equilibrium state, without taking into account the time which a system requires for the transition from an initial to a final state. Thus, only the thermodynamics of irreversible processes can be used to describe processes which lead to the formation of self-organising systems. Here, the time factor, and thus also the rate at which material reactions occur, is taken into account. Evolutionary processes are irreversibly coupled with temporal sequences, so that classical thermodynamics no longer suffices to describe them (Schuster and Sigmund, 1982). 

Statistical Mechanics and Thermodynamics of Irreversible Processes, Variational Principles in (Ono). ... 

Eysselberghe, 1963] P. Van Rysselberghe, Thermodynamics of Irreversible Process, p. 63, Hermann, Paris Blaisdell Publ. Co., London, (1963). 

In the following years, Prigogine developed various additional aspects of the new thermodynamics. He published in 1955 the little treatise Introduction to Thermodynamics of Irreversible Processes (LS.6), which was very successful and was translated into many languages. 

THL.27.1. Prigogine, On some aspects of Thermodynamics of Irreversible Processes, Proceedings International Conference on Theoretical Physics, Kyoto and Tokyo, Sept. 1953, pp. 475 87. 

TNC.4. I. Prigogine, Thermodynamics of Irreversible Processes and Fluctuations, Temperature 2, 215-232 (1955). 

TNC.7. I. Prigogine, Evolutionsprobleme in der Thermodynamik irreversibler Prozesse (Evolution problems in thermodynamics of irreversible processes), Z. Chemie 1, 203-208 (1961). 

Lars Onsager United States, b. Norway thermodynamic of irreversible processes... 

For most problems one needs to know how the elements of the second-order shear tensor are related to the velocity gradients and the coefficient of viscosity. It may be shown from the thermodynamics of irreversible processes (G12, C12, Bll) that for a Newtonian fluid the diagonal and nondiagonal elements of t have the form... 

From the point of view of thermodynamics we have now a microscopic model of entropy (see Eq. (52)). Therefore, we can verify that it leads to the basic expressions of thermodynamics of irreversible processes in the neighborhood of equilibrium.29 These expressions were derived until recently in the weakly coupled limit, or for dilute gases. 

A final remark should be made as to the validity of eq. (2.13). This equation suggests the existence of a set of independent relaxation mechanisms. A general proof for the existence of such mechanisms could be given for visco-elastic solids in terms of the thermodynamics of irreversible processes (52) at small deviation from equilibrium. For liquid systems, however, difficulties arise from the fact that in these systems displacements occur which are not related to the thermodynamic functions. 

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