Non-equilibrium steady state

Another possibility is that a system may be held in a constrained equilibrium by external forces and thus be in a non-equilibrium steady state (NESS). In this case, the spatio-temporal correlations contain new ingredients, which are also exemplified in section A3.3.2. 

The evaluative fugacity model equations and levels have been presented earlier (1, 2, 3). The level I model gives distribution at equilibrium of a fixed amount of chemical. Level II gives the equilibrium distribution of a steady emission balanced by an equal reaction (and/or advection) rate and the average residence time or persistence. Level III gives the non-equilibrium steady state distribution in which emissions are into specified compartments and transfer rates between compartments may be restricted. Level IV is essentially the same as level III except that emissions vary with time and a set of simultaneous differential equations must be solved numerically (instead of algebraically). 

A small square wave modulation of the current is applied in order to disturbe the non-equilibrium steady state of the discharge. The exponential decay of the concentrations leads to characteristic relaxation times, which allow the calculation of rate constants used in the modeling of the deposition mechanism. 

Wolery T. I (1986). Some Forms of Transition State Theory, Including Non-Equilibrium Steady State Forms Lawrence Livermore Laboratory, Livermore, Cal., UCRL-94221. 

Finally, the quest to develop mechanistic explanations for these varied and fascinating phenomena can succeed only if more data become available on the component processes. Kinetics studies of the reactions which make up a complex oscillatory system are essential to its understanding. In some cases, traditional techniques may be adequate, though in many others, fast reaction methods will be required. There also appears to be some promise in developing an analysis of the relaxation of flow systems in non-equilibrium steady states as a technique to complement equilibrium relaxation techniques. 

To determine how flux and free energy are related for systems not in equilibrium we consider, without loss of generality, the case where Nb/Na < Keq and J > 0. In a non-equilibrium steady state Na and Nb are held constant by pumping A molecules into the system, and pumping B molecules out of the system, at the steady state flux rate J. 

Thus it is trivial that Equation (3.9) holds in equilibrium. The more interesting case is a non-equilibrium steady state for which... 

Thermodynamic equilibrium is a special-case steady state that is obtained by closed systems. Open systems with steady (constant) transport fluxes may approach stable steady states that are not equilibrium states. For example, a non-equilibrium steady state is achieved by the system ofEquations (3.15) when J1/ = —J = J = constant. As in the case of the closed system, = 0 and [A] + [B] = X0... 

Enzyme-catalyzed reactions cycles, transients, and non-equilibrium steady states... 

There is almost no biochemical reaction in a cell that is not catalyzed by an enzyme. (An enzyme is a specialized protein that increases the flux of a biochemical reaction by facilitating a mechanism [or mechanisms] for the reaction to proceed more rapidly than it would without the enzyme.) While the concept of an enzyme-mediated kinetic mechanism for a biochemical reaction was introduced in the previous chapter, this chapter explores the action of enzymes in greater detail than we have seen so far. Specifically, catalytic cycles associated with enzyme mechanisms are examined non-equilibrium steady state and transient kinetics of enzyme-mediated reactions are studied an asymptotic analysis of the fast and slow timescales of the Michaelis-Menten mechanism is presented and the concepts of cooperativity and hysteresis in enzyme kinetics are introduced. 

When an enzyme-catalyzed biochemical reaction operating in an isothermal system is in a non-equilibrium steady state, energy is continuously dissipated in the form of heat. The quantity J AG is the rate of heat dissipation per unit time. The inequality of Equation (4.13) means that the enzyme can extract energy from the system and dissipate heat and that an enzyme cannot convert heat into chemical energy. This fact is a statement of the second law of thermodynamics, articulated by William Thompson (who was later given the honorific title Lord Kelvin), which states that with only a single temperature bath T, one may convert chemical work to heat, but not vice versa. 

Metabolic fluxes are responsible for maintaining the homeostatic state of the cell. This condition may be translated into the assumption that the metabolic network functions in or near a non-equilibrium steady state (NESS). That is, all of the concentrations are treated as constant in time. Under this assumption, the biochemical fluxes are balanced to maintain constant concentrations of all internal metabolic species. If the stoichiometry of a system made up of M species and N fluxes is known, then the stoichiometric numbers can be systematically tabulated in a... 

In addition to the stoichiometric mass-balance constraint, constraints on reaction fluxes and species concentration arise from non-equilibrium steady state biochemical thermodynamics [91]. Some constraints on reaction directions are... 

The probability distribution in Figure 11.6 indicates that there are two stable states for the chemical reaction system of Equation (11.25). Since the system is open to species A, B, and C, these states are non-equilibrium steady states (NESS). A more careful discussion of the terminology is in order here. The concept of an NESS has different meanings depending on whether we are considering a macroscopic or a microscopic view. This difference is best understood in comparison to the term chemical equilibrium. From a macroscopic standpoint, an equilibrium simply means that the concentrations of all the chemical species are constant, and all the reactions have no net flux. However, from a microscopic standpoint, all the concentrations are fluctuating. 

The concentrations fluctuate in a non-equilibrium steady state as well. In fact, the concentrations may fluctuate around multiple probability peaks, as illustrated in Figure 11.6. This system tends to fluctuate around one state, and then occasionally jump to the other. The situation is quite analogous to the transitions between two conformational states of a protein and the local fluctuations within the conformational states. 

The various forms of the sugars must also be considered in such processes as transport through membranes. If one form is exclusively (or even preferentially) transferred, the concentrations on each side of the membrane will not be expressed by the total concentrations (as usually measured), especially if the rates of mutarotation are different on both sides of the membrane. Keston has explained active transport of sugars across the membranes of the kidney and intestine on this basis, but assumed that an active form (the aldehydo form) is present in only a small proportion.305 320 The concept seems theoretically sound under non-equilibrium, steady-state conditions, but it cannot be applied to the reversal of the concentration gradient of a particular anomer. 

The earth and its living organisms are in a non-equilibrium state, but should maintain a steady state (homeostasis). In order to maintain a non-equilibrium steady state, it is important that the system is not closed but open to the outside. Only under open conditions can such non-equilibrium but steady states be maintained. If the earth were closed, all living things and our civilization would come to a catastrophe, but the earth is fortunately open to the universe, especially to solar irradiation. Based on this and on the first and second laws of thermodynamics, it was inevitable that we should meet a problem of environmental and energy resources while we rely on energy cycles condueted in the closed earth. It is important for our future civilization that the earth is open to the universe, i.e. to the sun. 

Open system is always in non-equilibrium. A closed system can be in non-equilibrium depending on the circumstances. It may have subsystems between which exchange of matter and energy can take place or in the system itself, thermodynamic variables may not be constant in space. A typical example of the former type is thermo-osmosis, which is discussed in Chapter 3, where the two subsystems are separated by a membrane. Example of the latter type is thermal diffusion, which has been discussed in Chapter 5. When the flows and counter-flows in opposite directions are generated by corresponding gradients, steady state is obtained. Both equilibrium and non-equilibrium steady states are time-invariant states, but in the latter case both flows and gradients are present. 

Non-equilibrium thermodynamics (NET) as it developed turned out to be quite useful in basic understanding of non-equilibrium steady states close to equilibrium and also in the region far from equilibrium. The theoretical and experimental studies can serve as a model for studies of similar type of real systems including biological, social and economic systems. 

Dufour effect Establishment of steady temperature gradient due to fixed concentration gradient. There can be two types of time-invariant states. One such is equilibrium state. In the equilibrium state, thermodynamic variables such as temperature T, pressure P and chemical potentials p, are adjusted in a way so that there is no (i) flow of matter, (ii) flow of energy and current and (iii) occurring in the system. Typical examples are vapour-liquid, liquid-Uquid, solid-liquid and chemical equilibria. However, time-invariant non-equilibrium steady states are also possible when opposite flows are balanced and gradients are maintained constant. 

The concept of equilibrium is quite commonly used in macro- and micro-economics. In fact, in natural systems, one can only expect unstable dynamic equilibrium. It may be noted that one can have stable non-equilibrium steady states. Approach to the so-called equilibrium or to such steady states would depend on a number of variables, which have to be carefully identified. Cause Effect relationship leads to the concept of Force Flux discussed in Part One in this book which is quite relevant for real systems. In the steady state, balance of forces occurs leading to balancing of effects. Typical example in economics is demand-supply relationship in the context of time variations in price and production. 

Recently, a non-equilibrium statistical thermodynamic theory based on stochastic kinetics has been formulated which has been applied to isothermal non-equilibrium steady state for biological systems [4]. Rate equations in terms of the probabilities of enzyme concentration are used instead of concentration. Expressions for the Gibbs free energy and entropy for the isothermal system are obtained in terms of dynamic cyclic reaction. 

NEMD has been employed for investigation of transport properties and models for non-equilibrium steady states. It has also been used for obtaining formal solution of... 

I3/I4 lumped one-stage open non-equilibrium steady state/dynamic... 

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