Reversible and Irreversible Dynamic Processes

In chemistry the term dynamic implies changing with time. Dynamic physical and chemical processes are of two basic types, irreversible and reversible. 

Irreversible processes are normally encountered in the context of chemical reactions. When the free energy (G°) of the product(s) of a reaction is sufficiently lower than the free energy of the reactant(s), the final (equilibrium) reaction mixture will comprise essentially all product(s) and no reac-tant(s). For example, a free-energy difference as little as 5 kcal/mol (ca. 21 kJ/mol) means the equilibrium mixture will consist of 99.97% products at 25°C [Eq. (2.8)]. In such cases, we can regard the reaction as essentially irreversible, that is, going in only one direction, or going to completion.  

When studying irreversible reactions by NMR, it is often useful to include an internal standard, an inert substance added to the reaction mixture at the beginning of the reaction. 

In Chapter 11 we will discuss a special class of irreversible reactions that involve radical-pair intermediates. Such reactions give rise to some very odd-looking NMR spectra. 

A reversible process is one in which a molecule (or set of molecules) changes back and forth between two (or more) different structures (e.g., different conformations, different stereoisomers, even different structural isomers), forming an equilibrium mixture of both (or all) the structures. Recall that although the concentration of each component of an equilibrium mixture does not change with time, equilibrium is nonetheless dynamic because interconversion between the components continues at rates that preserve the composition of the mixture. 

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Richter S (2006) Contributions to the dynamical behavior of cross-linked and cross-linking systems stimulus-sensitive microgels and hydrogels, reversible and irreversible gelation processes. Habilitation thesis, TU Dresden... 

The transient fluctuation theorem is applied to the transient response of a system. It bridges the microscopic and macroscopic domains and links the time-reversible and irreversible description of processes. In transient fluctuations, the time averages are calculated from a zero time with the known initial distribution function until a finite time. The initial distribution function may be, for example, one of the equilibrium distribution functions of statistical mechanics. So, for arbitrary averaging times, the transient fluctuation theorems are exact. The transient fluctuation theorem describes how irreversible macroscopic behavior evolves from time-reversible microscopic dynamics as either the observation time or the system size increases. It also shows how the entropy production can be related to the forward and backward dynamical randomness of the trajectories or paths of systems as characterized by the entropies per unit time. 

Fourier s law was the first example describing an irreversible process. There is a privileged direction of time as heat flows according to Fourier s law, from higher to lower temperature. This is in contrast with the laws of Newtonian dynamics in which past and future play the same role (time enters in Newton s law only through a second derivative, so Newton s law is invariant with respect to time inversion t —t). It is the Second Law of thermodynamics which expresses the difference between reversible and irreversible processes through the introduction of entropy. Irreversible processes produce entropy. 

Transient 2D-IRS has been used to study the dynamics of reversible and irreversible processes that are initiated by an external force typical investigations have included temperature jump (T-jump) [102] and flash photolysis experiments... 

Dual Lanczos transformation theory is a projection operator approach to nonequilibrium processes that was developed by the author to handle very general spectral and temporal problems. Unlike Mori s memory function formalism, dual Lanczos transformation theory does not impose symmetry restrictions on the Liouville operator and thus applies to both reversible and irreversible systems. Moreover, it can be used to determine the time evolution of equilibrium autocorrelation functions and crosscorrelation functions (time correlation functions not describing self-correlations) and their spectral transforms for both classical and quantum systems. In addition, dual Lanczos transformation theory provides a number of tools for determining the temporal evolution of the averages of dynamical variables. Several years ago, it was demonstrated that the projection operator theories of Mori and Zwanzig represent special limiting cases of dual Lanczos transformation theory. 

Therefore, the pharmacokinetic parameters, which can be derived from blood level measurements, are important aids to the interpretation of data from toxicological dose-response studies. The plasma level profile for a drug or other foreign compound is therefore a composite picture of the disposition of the compound, being the result of various dynamic processes. The processes of disposition can be considered in terms of "compartments." Thus, absorption of the foreign compound into the central compartment will be followed by distribution, possibly into one or more peripheral compartments, and removal from the central compartment by excretion and possibly metabolism (Fig. 3.23). A very simple situation might only consist of one, central compartment. Alternatively, there may be many compartments. For such multicompartmental analysis and more details of pharmacokinetics and toxicokinetics, see references in the section "Bibliography." The central compartment may be, but is not necessarily, identical with the blood. It is really the compartment with which the compound is in rapid equilibrium. The distribution to peripheral compartments is reversible, whereas the removal from the central compartment by metabolism and excretion is irreversible. 

Adsorption of vapors on test chamber walls has been previously described by means of models including two or three rate constants for adsorption/desorption processes in the ease of dynamic experiments (Dunn et al., 1988 Colombo et al., 1993) and with three adsorption/desorption constants in the case of static experiments (Colombo et al., 1993). Two rate constants describe a reversible sink whereas three rate constants describe a reversible and an irreversible (i.e. leak type) sink. However, these models did not adequately describe the sorption process(es), especially in the case of long-term tests, as resulted from two observations (Colombo et al., 1993) (a) the model with three sorption rate constants (reversible + irreversible sink) provided a better description of the experimental data than the one-sink model and (b) desorption experiments following adsorption gave strong indications that the irreversible sink was in fact slowly rever-... 

We emphasize that the processes depicted in Figure 1 and discussed above are more dynamic than could be presented in a two-dimensional diagram. We would also emphasize that this framework is not a molecular pathway —none of the arrows represent a specific biochemical mechanism. Rather, this framework temporally oig anizes the many cellular responses that have been observed after cells incur DNA damage. In particular, the framework highlights the importance of transitions from reversible to irreversible events and how the status of DNA repair may control these transitions. At the end of the chapter, we will discuss two alternative models for how DNA repair may coordinate the checkpoint and death responses to damage. Before those discussions, we will summarize briefly the current knowledge on several key players in the DNA damage response network. 

The accumulation is a dynamic process that may turn into a steady state in stirred solutions. Besides, the activity of accumulated substance is not in a time-independent equilibrium with the activity of analyte in the bulk of the solution. All accumulation methods employ fast reactions, either reversible or irreversible. The fast and reversible processes include adsorption and surface complexation, the majority of ion transfers across liquid/liquid interfaces and some electrode reactions of metal ions on mercury. In the case of a reversible reaction, equilibrium between the activity of accumulated substance and the concentration of analyte at the electrode surface is established. It causes the development of a concentration... 

Isolated-molecule dynamics is expected to be a sufficiently elementary process to permit observation of microscopic reversibility in the dynamics and, hence, to display a dependence of the outcome of dynamics on initial conditions. This dependence is desirable since the ability to retain information about initial conditions is necessary in order to achieve the technologically desirable goal of externally influencing chemical reactions. However, a great many experiments, perhaps with insufficiently well-characterized preparation and measurement, have indicated that time-irreversible relaxation is a useful model for many intramolecular processes. Thus, isolated-molecule intramolecular dynamics serves as a laboratory for the study of the inter-relationship between irreversible relaxation behavior in systems that are fundamentally de-scribable by time-reversible equations of motion. It also presents an experimental challenge to prepare sufficiently well-characterized states to observe time reversibility and sensitivity to initial conditions. 

Equilibrium versus conservation. The notion of static equilibrium is to proscribe, if one is interested in better understanding the notion of reversibility and related concepts, such as the role of time, the distinction between dynamic and static, the separation thermodynamics—thermodynamics of irreversible processes, etc. In replacing this notion of static equilibrium by a rule of conservation, one has access to a more interesting conceptual level. 

Time-reversibility of irreversible processes sounds paradoxical and requires some explanation (Yablonsky et al., 2011b). The most direct interpretation of time-reversing is to go back in time. This means taking a solution of the dynamic equations x t) and checking whether x(—t) is also a solution. For microscopic dynamics (the Newton or Schrbdinger equations), we expect this to be the case. Nonequilibrium statistical physics combines this idea with the description of macroscopic or mesoscopic kinetics by an ensemble of elementary processes (reactions). The microscopic reversing of time at this level turns into reversing of arrows the reaction a, A, —> Eft , transforms into... 

Such an attitude to equilibrium thermodynamics - the science which revealed irreversibility of the evolution of isolated systems and asymmetry of natural processes with respect to time - is related to some circumstances that require a thorough analysis. Here we will emphasize only one of them which is the most important for imderstanding further text. It lies in the fact that the most important notion of thermodynamics, i.e. equilibrium, became interpreted exclusively as the state of rest (absence of any forces and flows in the thermodynamic system) and equilibrium processes - as those identical to reversible ones. These one-sided interpretations ignored the Galileo principle of relativity, the third law of Newton and the Boltzmann probabilistic interpretations of entropy that allow dynamic interpretations of equilibria and irreversible interpretations of equilibrium processes. 

It is important to stress that the combination of both the low-Q QENS data and MD simulations allows us to understand on a molecular basis the onset of the reversible folding and the successive irreversible denaturation. In particular, by considering these results and the cited NMR and FTIR experimental data [15,19] it is possible to conclude that the denaturation of the protein and the dynamic crossover in its hydration water are causally related. In fact, all of their coincidences suggest that this high-r crossover could be a significant factor in the reversible denaturation process. We also note that the organization of water/biomolecules... 

It was the first evolutionary formulation of cosmology. This was a revolutionary statement as the existence of irreversible processes (and therefore of entropy) conflicts with the time-reversible view of dynamics. Of course, classical dynamics has been superseded by quantum theory and relatively. But this conflict remains because in both quantum theory and relativity the basic dynamical laws are time-reversible. 

The general phenomenon of polymer adsorption/retention is discussed in some detail in Chapter 5. In that chapter, the various mechanisms of polymer retention in porous media were reviewed, including surface adsorption, retention/trapping mechanisms and hydrodynamic retention. This section is more concerned with the inclusion of the appropriate mathematical terms in the transport equation and their effects on dynamic displacement effluent profiles, rather than the details of the basic adsorption/retention mechanisms. However, important considerations such as whether the retention is reversible or irreversible, whether the adsorption isotherm is linear or non-linear and whether the process is taken to be at equilibrium or not are of more concern here. These considerations dictate how the transport equations are solved (either analytically or numerically) and how they should be applied to given experimental effluent profile data. 

One essential aspect in evaluating the presence of these compounds in different matrices is that when added to foods they often disappear as a result of reversible and/ or irreversible chemical reactions. When sulfites are added to foods, they come into contact with an aqueous medium there and undergo a process of dissociation in which the oxyanions may be separated from their cations depending on the pH, ionic strength and temperature of the medium. This process produces a dynamic chemical balance among species (sulfur dioxide, sulfurous acid, and sulfite and bisulfite anions) that tends toward the formation of one or another depending on the conditions in the medium so that all the forms coexist but in different proportions in different conditions (Wedzicha, 1992 Margarete et al., 2006). 

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