Nonequilibrium process thermodynamics

Keizer J 1987 Statistical Thermodynamics of Nonequilibrium Processes (New York Springer)... 

In nonequilibrium steady states, the mean currents crossing the system depend on the nonequilibrium constraints given by the affinities or thermodynamic forces which vanish at equihbrium. Accordingly, the mean currents can be expanded in powers of the affinities around the equilibrium state. Many nonequilibrium processes are in the linear regime studied since Onsager classical work [7]. However, chemical reactions are known to involve the nonlinear regime. This is also the case for nanosystems such as the molecular motors as recently shown [66]. In the nonlinear regime, the mean currents depend on powers of the affinities so that it is necessary to consider the full Taylor expansion of the currents on the affinities ... 

In this chapter, we have described recent advances in nonequilibrium statistical mechanics and have shown that they constitute a breakthrough which opens very new perspectives in our understanding of nonequilibrium processes and the second law of thermodynamics. 

It is most remarkable that the entropy production in a nonequilibrium steady state is directly related to the time asymmetry in the dynamical randomness of nonequilibrium fluctuations. The entropy production turns out to be the difference in the amounts of temporal disorder between the backward and forward paths or histories. In nonequilibrium steady states, the temporal disorder of the time reversals is larger than the temporal disorder h of the paths themselves. This is expressed by the principle of temporal ordering, according to which the typical paths are more ordered than their corresponding time reversals in nonequilibrium steady states. This principle is proved with nonequilibrium statistical mechanics and is a corollary of the second law of thermodynamics. Temporal ordering is possible out of equilibrium because of the increase of spatial disorder. There is thus no contradiction with Boltzmann s interpretation of the second law. Contrary to Boltzmann s interpretation, which deals with disorder in space at a fixed time, the principle of temporal ordering is concerned by order or disorder along the time axis, in the sequence of pictures of the nonequilibrium process filmed as a movie. The emphasis of the dynamical aspects is a recent trend that finds its roots in Shannon s information theory and modem dynamical systems theory. This can explain why we had to wait the last decade before these dynamical aspects of the second law were discovered. 

A number of assumptions are involved in the derivation of the mathematical expressions for nucleation. First, the change of one phase into another is really a nonequilibrium process. There is no guarantee that equations derived for thermodynamic equilibrium will be valid when applied to nonequilibrium. For example, the relationship between surface tension and radius applies for a static bubble, but does it apply to a bubble which is changing in size Second, it is imagined that any cluster which grows to a nucleus is bodily removed from the liquid. Thus nuclei cannot accumulate. This idea leads to a chopped distri-... 

Much of the pre-Gibbsian development of thermodynamics (Chapters 3 and 4) is formulated in terms of nonequilibrium processes, involving the left-hand side of (2.65). This pre-Gibbsian terrain must be traversed in order to understand the historical roots,... 

It is true that in his own work De Donder did not pursue the consequences of nonequilibrium very far. We have to wait until the basic discovery of Onsager s reciprocity relations in 1931 and till the work of Eckart, Meixner, and many others in the 1940s and the 1950s to see thermodynamics of nonequilibrium processes take shape and be integrated into common knowledge. 

Thermodynamic analysis is a useful tool in understanding CVD processes but should be used with caution and careful attention to the assumptions underlying the application. Because CVD is a nonequilibrium process, the thermodynamic predictions are often only semiquantitative and mainly serve to provide insights into the process. Accurate process prediction must include chemical kinetics and transport rate considerations. 

The ultracentrifuge can be used to separate fractions of different molecular weights in a mixture of solutes and to determine the molecular weight of a solute. Two different approaches can be taken. In the sedimentation velocity approach, the change in the concentration profile with time is determined during the centrifugation process. This nonequilibrium process requires a knowledge of diffusion rates and is not based directly on thermodynamics. We will leave a discussion of this process to other texts. 

Keizer, J. Statistical thermodynamics of nonequilibrium processes. Springer-Verlag, Berlin, 1987. 

S. Wisniewski, B. Stainszewski, and R. Szymanik, Thermodynamics of Nonequilibrium Processes, Reidel, Boston, 1976. 

The next sphere of competition between equilibrium and nonequilibrium thermodynamics is the analysis of irreversible trajectories. A popular opinion about the possibility for the equilibrium thermodynamics only to determine admissible directions of motion for nonequilibrium processes was already mentioned in Introduction. However, the more... 

Errors in the description of nonequilibrium processes in the linear nonequilibrium thermodynamics (Glansdorff et al., 1971 Kondepudi et al., 2000 Prigogine, 1967 Zubarev, 1998) are caused primarily by the assumptions (unnecessary at MEIS application) on the linearity of motion equations. One of the main equations of this thermodynamics has the form... 

Zubarev, D.N., "Thermodynamics of Nonequilibrium Processes. Physical Encyclopedia", pp. 87-89. Bolshaya Rossiiskaya Entsyklopedia, Moscow, Vol. 5 (1998). (in Russian). 

The thermodynamic approach considers micropores as elements of the structure of the system possessing excess (free) energy, hence, micropore formation processes are described in general terms of nonequilibrium thermodynamics, if no kinetic limitations appear. The applicability of the thermodynamic approach to description of micropore formation is very large, because this one is, in most cases, the result of fast chemical reactions and related heat/mass transfer processes. The thermodynamic description does not contradict to the fractal one because of reasons which are analyzed below in Sec. II. C but the nonequilibrium thermodynamic models are, in most cases, more strict and complete than the fractal ones, and the application of the fractal approach furnishes no additional information. If no polymerization takes place (that is right for most of processes of preparation of active carbons at high temperatures by pyrolysis or oxidation of primary organic materials), traditional methods of nonequilibrium thermodynamics (especially nonequilibrium statistical thermodynamics) are applicable. 

Thermodynamics of nonequilibrium (irreversible) processes is an extension of classical thermodynamics, mainly to open systems. Unfortunately, the Second Law of classical thermodynamics cannot be applied directly to systems where nonequilibrium (i.e., thermodynamically irreversible) pro cesses occur. For this reason, thermodynamics of nonequilibrium processes has used several principal concepts that are supplementary to the classical thermodynamics postulates. In contrast to the postulates, many of the con cepts in thermodynamics of nonequilibrium processes can be mathe maticaUy substantiated by considering, for example, the time hierarchy of the processes involved. 

In this book, we shall always imply that the nonequilibrium state occurs at the macroscopic level. However, at the microscopic level, fast processes of thermal relaxation run into each microscopic (physically small) part of the system. These processes bring this physically small part of the system to a state that is thermodynamically stable, the relaxation being much faster than the other nonequilibrium processes under consideration. 

The thermodynamic force (affinity) X is a pivotal concept in thermo dynamics of nonequilibrium processes because of its relationship to the concept of driving force of a particular irreversible process. Evidently, thermodynamic forces arise in spatially inhomogeneous systems with, for example, temperature, concentration, or pressure inhomogeneity. In spatially uniform homogeneous systems, such forces arise either in the presence of chemically reactive components that have not reached thermodynamic equiHbrium via respective chemical transformations or at the thermodynamic possibility of some phase transformations. 

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