Theory of irreversible processes

Kubo R, Yokota M and Nakajima S 1957 Statistical-mechanical theory of irreversible processes. Response to thermal disturbance J. Phys. Soc. Japan 12 1203... 

As an introduction to the peculiar properties of the spin Hamiltonians, we first give a short summary of the theory of spin relaxation in liquids where the problem is in fact a Brownian motion one. Then we consider the many-spin problem in solids and apply the general formalism of the theory of irreversible processes developed by Prigogine and his co-workers. We also analyse some aspects of the recent work of Caspers and Tjon on this subject. Finally, we indicate the special interest of spin-spin relaxation phenomena in connection with non-Markovian processes. 

MSN.89.1. Prigogine and A. Grecos, The dynamical theory of irreversible processes. Proceedings, International Conference Frontiers of Theoretical Physics, Calcutta, 1977, F. C. Auluck, L. S. Kothari, V. S. Nanda, eds., pp. 51-62. 

MSN.91. I. Prigogine and A. Grecos, On the dynamical theory of irreversible processes and the microscopic interpretation of nonequihbrium entropy. Proceedings, I3th lUPAP Conference on Statistical Physics, Ann. Israel Phys. Soc. 2, 84—97, 1978. 

MSN.94. I. Prigogine, The microscopic theory of irreversible processes, in Proceedings, 11th Symposium Parked Gas Dynamics, Vol. 1, CEA, Paris, 1979, pp. 1-27. 

Ilya Prigogine, the founding editor of Advances in Chemical Physics, died May 25, 2003. He was born in Moscow, fled Russia with his family in 1921, and, after brief periods in Lithuania and Germany, settled in Belgium, which was his home for 80 years. His many profound contributions to the theory of irreversible processes included extensions of both macroscopic thermodynamic analysis and statistical mechanical analysis of time-dependent processes and the approach to equilibrium. While sometimes controversial, these contributions were uniformly of outstanding intellectual merit and always addressed to the most fundamental issues they earned him international repute and the Nobel Prize in Chemistry in 1977. Arguably equally important was his creation of a school of theoretical chemical physics centered at the University of Brussels, as well as the mentoring of numerous creative and productive scientists. 

This completes our summary of probabilistic and physical approaches to the theory of irreversible processes. As we have seen, probabilistic models are of great use in the description of irreversible processes but their ultimate justification rests on physical studies and approximations. 

It turned out that many physicists often confused two essentially different problems (a) the relative probabilities of a decrease and of an increase of the //-function starting from a given value of H (which is different from the minimum value) and (b) the relative probabilities of a transition of the H-function from a higher to a lower value and of a transition in the opposite direction. The difference between these two problems I discussed in a paper, On a Misconception in the Probability Theory of Irreversible Processes (Proc. Amst. Acad., vol. 38, 1925). 

Riseman, J and J. G. Kirkwood The statistical mechanical theory of irreversible processes in solutions of macromolecules. In Rheology, edited by F. R. Eirich, Vol. I, pp. 495—523, New York Academic Press 1956. 

If transformations (5.3.7) are used, the complex compliance Z(ito) should be given as an analytical function of u> on the whole complex plane. As the theory of irreversible processes shows, Z(iw) (and, hence, F(r/)) should exhibit some properties resulting from general principles of dynamics (e.g. the principle of causality) and the Kramers-Kronig reciprocal equations l... 

R. Kubo, /. Phys. Soc. Jpn., 12, 570 (1957). Statistical Mechanical Theory of Irreversible Processes. I. General Theory and Simple Application to Magnetic and Conduction Problems. 

R. Kubo (1957) Statistical-mechanical theory of irreversible processes. 1. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. (Japan) 12, 570-586 R. Kubo (1966) The fluctuation-dissipation theorem. Repts. Prog. Phys. 29, pp. 255-284... 

Kubo R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J Phys Soc Jpn 1957 12 570-586. 

Molecular fragments are the mutually open subsystems, which exhibit fluctuations in their electron densities and overall numbers of electrons. In chemistry one is interested in both the equilibrium distributions of electrons and non-equilibrium processes characterized by rates. Recently, it has been demonstrated [23] that the information theory provides all necessary tools for the local dynamical description of the density fluctuations and electron flows between molecular subsystems, which closely follows the thermodynamic theory of irreversible processes [146],... 

In this review we discuss some topics in the theory of irreversible processes [1-5], as they relate to the developing field of liquid phase chemical dynamics [6]. 

Section II gives an overview of the central issues, restricted to the specific problem of atomic motion in fluids. In the Appendix, this overview is expanded into a discussion of the general theory of irreversible processes [1-5], focusing especially on Onsager s work [1,3,4], including its extension to finite memory due to Mori [5]. 

In contrast, the particle s fast variable equation of motion is nonclassical and a potential V S-,x) that is very different from VF(S x) drives the dynamics. (Similar problems occur in the general theory of irreversible processes. There they are resolved by assuming slow variable relaxation [1-5], see Appendix.)... 

At first glance a review of Onsager s theory might appear to have little or no relevance to the topics of this chapter. This, however, is not the case. This is because Onsager s theory, as extended to include memory by Mori [5] is the most general slow variable theory of irreversible motion. Thus, our examination of Onsager s work exposes limitations inherent in all slow variable models. Especially, it shows that the limitations of the Kramers-type models for reactions merely reflect the macroscopic scope of the general theory of irreversible processes [1,3-5]. 

The foundations for the macroscopic approach to non-equilibrium thermod5mamics are found in Einstein s theory of Brownian movement [1] of 1905 and in the equation of Langevin [2] of 1908. Uhlenbeck and Omstein [3] generalized these ideas in 1930 and Onsager [4, 5] presented his theory of irreversible processes in 1931. Onsager s theory [4] was initially deterministic with little mention of fluctuations. His second paper... 

We first review in brief those elements of the Onsager theory of irreversible processes (e.g., Reference 37) which are necessary for our development. In general, it may be stated that we observe in nature many irreversible processes which behave such that ... 

It is a truism that the theory of irreversible processes is more difficult and less general than the theory of equiUbrium states. However, it happens on occasion that the theory of an equilibrium quantity is so rudimentary that a generalization of the theory to dynamic measurement seems straightforward and almost inevitable. This situation occurs in the present theory of the heat capacity, which is taken as the basis of a theory of anomalous sound propagation in the critical region. 

Abstract Based on the theory of irreversible process thermodynamics, non-linear stress-strain-temperature equations are derived, together with an expression for time-temperature equivalence. In addition, an equation of shift factor for time-temperature equivalence is also obtained. The parameters in the equations are experimentally determined and the main curves for creep compliance and cohesion of TOP granite are obtained by a series of creep tests. As a result, it is proved that both deformation and strength of the TOP granite follow the time-temperature equivalent principle. 

In this paper time-temperature equivalence for rocks is investigated for non-linear behaviours of rocks, based upon inner-variable theory of irreversible process and creep tests. 

In equilibrium thermodynamics model A and in model B not far from equilibrium (and with no memory to temperature) the entropy may be calculated up to a constant. Namely, in both cases S = S(V, T) (2.6)2, (2.25) and we can use the equilibrium processes (2.28) in B or arbitrary processes in A for classical calculation of entropy change by integration of dS/dT or dS/dV expressible by Gibbs equations (2.18), (2.19), (2.38) through measurable heat capacity dU/dT or state Eqs.(2.6>, (2.33) (with equilibrium pressure P° in model B). This seems to accord with such a property as in (1.11), (1.40) in Sects. 1.3, 1.4. As we noted above, here the Gibbs equations used were proved to be valid not only in classical equilibrium thermodynamics (2.18), (2.19) but also in the nonequilibrium model B (2.38) and this expresses the local equilibrium hypothesis in model B (it will be proved also in nonuniform models in Chaps.3 (Sect. 3.6), 4, while in classical theories of irreversible processes [12, 16] it must be taken as a postulate). 

Extensions of variational methods to otha problems have yet to be tried. The approach is directly applicable to problems involving flowing systems, to equations encompassing coupled heat and mass transfer and to a wider thermodynamical treatment of chemmal systems in their entirety. This in its fullest form will allow thermal theory to be migrated in a general theory of irreversible processes. Under sucdi a scheme the dynamic (transient) behaviour of chemical reactions can be discxissed without recourse to the uniform Semenov-like conditions universal in contemporary treatments. 

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