Open systems far from equilibrium

M. Open System far from Equilibrium, Multiple Subprocesses, and Curved Spacetime... 

The open system far from equilibrium process of this invention thus allows electromagnetic power systems to be developed that permissibly exhibit a coefficient of performance (COP) of COP> 1.0. It allows electromagnetic power systems to be developed that permissibly (a) power themselves and their loads and losses, (b) self-oscillate, and (c) exhibit negentropy. 

Self-replication and mutagenicity in an open system far from equilibrium are thus sufficient to produce behavior patterns including selection and evolution. Even in relatively simple replication systems properties optimal with respect to the wild-type can be produced in vitro in a few generations. Such effects must be the consequence of a physical principle. Can such a principle be formulated quantitatively ... 

Note that the appearance of a generic time scale is a characteristic property of a dissipative system and T generates its time evolution in scaled time units. Such time operators are strictly speaking forbidden in standard Quantum Mechanics, see Ref. [24] for further aspects on the problem, however, in open systems far from equilibrium they do not only exist but might also be useful in many applications, see below and [4-10, 13-15], The form (15) has been investigated and obtained... 

Nicholas, J., K.R. Cameron R.W. Honess. 1992. Herpesvirus saimiri encodes homologues of G protein-coupled receptors and cyclins. Nature 355 362-5. Nicolis, G. 1971. Dissipative structures in open systems far from equilibrium. Adv. Chem. Phys. 19 209-324. 

Open systems far from equilibrium will be the subject of this chapter. This situation is, for example, given for catalytic reactions under steady-state flow conditions. Apart from oscillatory or chaotic kinetics as described in Chapter 7, the interplay between reaction and transport processes may lead to the formation of concentration patterns on mesoscopic... 

Nicolis, G. (1971), "Stability and dissipative structures in open systems far from equilibrium." Adv, Chern, Phys, 19, 209-324,... 

All these effects can be traced back to the common theoretical framework of nonlinear dynamics. We are dealing with open systems far from equilibrium for which the kinetics can be described by a set of coupled nonlinear ordinary differential equations of the form... 

In short, we must violate the Lorentz symmetric regauging condition during the excitation discharge represented by operation 2 of an open system far from thermodynamic equilibrium. 

In short, as a dipolar entity, the charge is an open system far from thermodynamic equilibrium in 3-space EM energy flow. Indeed, it has no input energy flow in 3-space, but instead has an input energy flow from the imaginary plane (from the time dimension). Hence classical 3-equilibrium thermodynamics does not apply. 

Particularly during its excitation discharge, the system must be an open thermodynamic system far from equilibrium in its energetic exchange with the active vacuum. In that case classical equilibrium thermodynamics does not apply, and such a system is permitted to... 

No laws of physics or thermodynamics are violated in such open dissipative systems exhibiting increased COP and energy conservation laws are rigorously obeyed. Classical equilibrium thermodynamics does not apply and is permissibly violated. Instead, the thermodynamics of open systems far from thermodynamic equilibrium with their active environment—in this case the active environment-rigorously applies [2-4]. 

The volume or space in which reaction occurs is called the reactor. Closed systems, for which matter is neither gained nor lost, are referred to in the engineering literature as batch reactors. An open, or flow reactor, which permits the flow of matter in and out of the system, allows for the continuous and convenient change of solution composition. Most importantly, the continuous flow of matter into and out of the flow reactor trivially solves the problem of maintaining the system far from equilibrium, while facilitating the detection and determination of the chemical properties of species in these states. 

Example 4.8 Chemical reactions and reacting flows The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. The determination of entropy of stationary states in a continuously stirred tank reactor may provide insight into the thermodynamics of open nonlinear systems and the optimum operating conditions of multiphase combustion. These conditions may be achieved by minimizing entropy production and the lost available work, which may lead to the maximum net energy output per unit mass of the flow at the reactor exit. 

When the system is out of full thermodynamic equilibrium, its non-equilibrium state may be characteristic of it with gradients of some parameters and, therefore, with matter and/or energy flows. The description of the spontaneous evolution of the system via non equilibrium states and prediction of the properties of the system at, e.g., dynamic equilibrium is the subject of thermodynamics of irreversible (non-equilibrium) processes. The typical purposes here are to predict the presence of solitary or multiple local stationary states of the system, to analyze their properties and, in particular, stability. It is important that the potential instability of the open system far from thermodynamic equilibrium, in its dynamic equilibrium may result sometimes in the formation of specific rather organized dissipative structures as the final point of the evolution, while traditional classical thermodynamics does not describe such structures at all. The highly organized entities of this type are living organisms. 

From the thermodynamic point of view, the systems under consideration are open and far from equilibrium state. Obviously, common physico-chemical methods of research and theoretical description fail to be helpful in this case. 

Prom the standpoint of thermodynamics, the system electrolyte-film-electrode is open and far from equilibrium state. In this study we use the theoretical approach to the description of such systems created by H. Poincare and further developed later by Andronov and others. This method is called bifurcation analysis or, alternatively, theory of non-linear dynamic systems [7]. It has been applied to the studies of macrokinetics (dynamics) of the processes in electrode film systems. 

The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. Determine the optimum operating conditions. 

Only in the last decades has the thermodynamics of open systems been treated intensively and successfully. The thermodynamics of irreversible systems was studied initially by Lars Onsager, and in particular by Ilya Progogine and his Brussels school both studied systems at conditions far from equilibrium. Certain systems have the capacity to remain in a dynamic state far from equilibrium by taking up free energy as a result, the entropy of the environment increases (see Sect. 9.1). 

In the course of time open systems that exchange matter and energy with then-environment generally reach a stable steady state. However, as shown by Glansdorff and Prigogine, once the system operates sufficiently far from equilibrium and when its kinetics acquire a nonlinear nature, the steady state may become unstable [15, 18]. Feedback regulatory processes and cooperativity are two major sources of nonlinearity that favor the occurrence of instabilities in biological systems. 

The interesting feature of our representation is that many sub-terms of the "fourth", non-linear, term may contain the "potential term" (the cyclic characteristic C) as well. It means that even in the domain "far from equilibrium" the open system still may have a "memory" about the equilibrium. Particular forms of this general Equation (77), i.e. for the cases of step limiting and the vicinity of equilibrium, respectively, are presented. 

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