Irreversible processes, equilibrium

In an irreversible process the temperature and pressure of the system (and other properties such as the chemical potentials to be defined later) are not necessarily definable at some intemiediate time between the equilibrium initial state and the equilibrium final state they may vary greatly from one point to another. One can usually define T and p for each small volume element. (These volume elements must not be too small e.g. for gases, it is impossible to define T, p, S, etc for volume elements smaller than the cube of the mean free... 

One may note, in concluding this discussion of the second law, that in a sense the zeroth law (thennal equilibrium) presupposes the second. Were there no irreversible processes, no tendency to move toward equilibrium rather than away from it, the concepts of thennal equilibrium and of temperature would be meaningless. 

Various constraints may be put on this expression to produce alternative criteria for the directions of irreversible processes and for the condition of equilibrium. For example, it follows immediately that... 

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. 

Tethering may be a reversible or an irreversible process. Irreversible grafting is typically accomplished by chemical bonding. The number of grafted chains is controlled by the number of grafting sites and their functionality, and then ultimately by the extent of the chemical reaction. The reaction kinetics may reflect the potential barrier confronting reactive chains which try to penetrate the tethered layer. Reversible grafting is accomplished via the self-assembly of polymeric surfactants and end-functionalized polymers [59]. In this case, the surface density and all other characteristic dimensions of the structure are controlled by thermodynamic equilibrium, albeit with possible kinetic effects. In this instance, the equilibrium condition involves the penalties due to the deformation of tethered chains. 

Since then, it has been observed that the dimerization of imidazolylidenes and triazolinylidenes does not occur at room temperature. In contrast, the dimerization of imidazolinylidenes is a fast and irreversible process but is prevented by using bulky nitrogen substituents. The benzimidazolylidenes are in equilibrium with the dimer, this equilibrium being affected by steric... 

The irreversible processes described must not occur even on open circuit. In a reversible cell, a definite equilibrium must be established and this may be defined in terms of the intensive variables in a similar way to the description of phase and chemical equilibria of electroneutral components. 

These results seemed to indicate that CO adsorption on platinum is an irreversible process, i.e. there is no equilibrium of the form Pt-COad COsol + Pt. The purpose of the following experiment was to check this hypothesis. 

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). 

Our "superheated liquid-film concept" stands on the thermodynamic basis of (1) equilibrium shifts due to reactive separation under boiling and refluxing conditions and (2) irreversible processes of heat flows through the catalyst layer as well as bubble formation from the catalyst surface. 

The relationships between the components of the Hantzsch triangle were considered in-depth in the monograph 2 and references therein. Although the problem of reactivity of ambident substrates has been studied over many years and from different points of view, the complexity of the starting system and its numerous reaction pathways do not allow one to reliably predict the results of O-alkylation in each particular case, because it is necessary to take into account the rates of numerous reversible and irreversible processes as well as the thermodynamic factors responsible for the position of the equilibrium it is necessary to take solvent effects into consideration when estimating the thermodynamic factors. All accumulated observations are approximated by several empirical mles included in monographs 2 and 3. 

The usual emphasis on equilibrium thermodynamics is somewhat inappropriate in view of the fact that all chemical and biological processes are rate-dependent and far from equilibrium. The theory of non-equilibrium or irreversible processes is based on Onsager s reciprocity theorem. Formulation of the theory requires the introduction of concepts and parameters related to dynamically variable systems. In particular, parameters that describe a mechanism that drives the process and another parameter that follows the response of the systems. The driving parameter will be referred to as an affinity and the response as a flux. Such quantities may be defined on the premise that all action ceases once equilibrium is established. 

Hence, when Tk is zero the system is in equilibrium, but for non-zero Tk an irreversible process that takes the system towards equilibrium, occurs. The quantity Tkl which is the difference between intensive parameters in entropy representation, acts as the driving force, or affinity of the non-equilibrium process. 

The sum is equal to zero for reversible processes, where the system is always under equilibrium conditions, and larger than zero for irreversible processes. The entropy change of the surroundings is defined as... 

GEN. 101. I. Prigogine, The microscopic theory of irreversible processes, in Proceedings, International Symposium, Self-Organization Autowaves and Structures far from Equilibrium, 1983, V. I. Krinsky, ed.. Springer, Berlin 1984, pp. 22-28. 

Natural phenomena are striking us every day by the time asymmetry of their evolution. Various examples of this time asymmetry exist in physics, chemistry, biology, and the other natural sciences. This asymmetry manifests itself in the dissipation of energy due to friction, viscosity, heat conductivity, or electric resistivity, as well as in diffusion and chemical reactions. The second law of thermodynamics has provided a formulation of their time asymmetry in terms of the increase of the entropy. The aforementioned irreversible processes are fundamental for biological systems which are maintained out of equilibrium by their metabolic activity. 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

Given the structural similarity of intermediates A and E, and also of B and D, it seems obvious that each reaction step in the cycle is potentially reversible. The equilibrium is shifted, however, into the desired direction by the steric shielding of the sacrificial hydrogen acceptor, which makes the reductive elimination of TBA an essentially irreversible process. 

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