Prigogine's Theory Research Articles

Rosenfeld-Prigogine complementarity of descriptions in the context of informational statistical thermodynamics

Within the framework of informational statistical thermodynamics, we consider the case of a particular dissipative dynamical system, namely, a system of harmonic oscillators weakly interacting with a thermal bath. Informational entropy and informational-entropy production are obtained. In terms of them we derive the information gain in alternative pictures and a Rosenfeld-like complementarity principle between microdescription and macrodescription. This complementarity is related to a kind of measure of the incompleteness of both descriptions and to Prigogine's theory of irreversible processes. The fundamental role of the universal Boltzmann constant for the characterization of this complementarity is discussed.

Description of the Glass Transition by a Percolation Blocking of Local Chemical Order

Abstract A model for the liquid-glass transition, based on a percolation blocking of local chemical order, is proposed. The case of metallic liquids and glasses, whose structure is dominated by first neighbour chemical arrangement, is first treated. The chemical ordering "reaction" of the liquid phase is studied at thermodynamical equilibrium and the increase of the chemical order parameter with decreasing temperature is calculated. Within a given composition interval, however, a geometrical percolation process is shown to block this reaction below a "percolation temperature" (corresponding to null cooling rate) where the liquid is irreversibly frozen into a glass. The liquid-glass "phase diagram" is established and kinetic arguments, involving "frustrated" finite clusters which are formed close to the percolation threshold, provide an evaluation of the experimentally measured "glass transition temperature" as a function of cooling rate. The validity of this one order parameter model is then discussed with the help of the irreversible thermodynamics theory of Prigogine. The formation of tetracoordinated glasses is explained by the formation of tetrahedral bonds, when the liquid temperature decreases, and represented by a "hole ordering" reaction. A general description of the structure of tetracoordinated glasses is thus achieved, which applies to amorphous silicon and germanium, 111 -V compounds, silica, amorphous water etc. Furthermore, an estimation of the temperature interval for the glass transformation of silica is obtained, which agrees well with experiment. The existence of frustrated clusters gives to glasses a composite structure in the "medium distance order", which could explain the "fractal nature" of glass fracture surfaces down to the nanometer scale.

Thermodynamics of the lower critical threshold line in solutions of cyclic and linear poly(dimethylsiloxane)s in tetramethylsilane

The main features of the critical line in presure-temperature-composition space for mixtures containing either a linear or a cyclic poly(dimethylsiloxane) (PDMS) in tetramethylsilane (TMS) are predicted through the use of the Patterson modification of Prigogine's corresponding-states theory, which incorporates the cell model of a liquid together with a simple van der Waals dependence of the configurational energy on volume. Two main kinds of critical lines are obtained: one is a continuous line for those mixtures with a small chain-length difference between the components, leading to a fairly good prediction of the liquid-vapour critical temperatures of the pure substances; and the other is a broken line for mixtures with a large chain-length difference between the polymer and solvent, indicating the occurrence of a lower critical threshold temperature ( LCTT) at low polymer concentrations. A full set of temperature and pressure reduction parameters for both linear and cyclic oligomers and PDMS are reported, and are used as the basis for all the calculations with no adjustment whatsoever. It is predicted that the system of minimum chain length to show an LCTT is that containing a PDMS of 24 skeletal bonds, compared to the methane-hexane system in the n-alkanes, thus giving an insight into the more flexible and more expanded nature of the PDMS series. Results for the interaction parametert χ 1 confirm that any difference in chemical nature between TMS and the PDMS series may be largely ignored since the structural term c 1 τ alone can account for the LCTT behaviour.

Thermodynamics of association of cholesterol in an aprotic solvent

The colligative properties of benzene solutions of cholesterol up to 0.25 mol kg–1 in the temperature range 298–333 K have been determined by vapour pressure osmometry. The relations for the concentration dependence of the osmotic coefficient, activity coefficient and excess thermodynamic functions are given in analytical form, in which the regression coefficients are correlated with the virial coefficients, which, according to the McMillan–Mayer theory, characterize the contributions arising from the formation of pairs, triplets etc. of solute particles in a definite medium. On the basis of Prigogine's theory for associated solutions it may be concluded that the solvent–solute interactions are weak. In addition, the non-ideal behaviour of the system investigated was discussed on the basis of an association model, including an extended series of multimers, the formation of which is described in terms of two independent parameters: the dimerization constant β2 and constant K. The values of the dimerization constant β2 and constant K were determined by the curve-fitting method, whereas the concentration of monomer was obtained via Bjerrum's integral. On the basis of van't Hoff's relation for the temperature dependence of the equilibrium constants, the thermodynamic functions of association processes were determined and are discussed with respect to the oligomeric species formed.

The netlike inference process and stability analysis

In this article, an inference process is defined as a series of events in which the truth values flow from propositions along certain inference channels. the concepts of netlike inference process and solution searching process are then described. the notion of excitedness is defined as a measure of the activeness of thinking. In the context of an inference process, excitedness describes the truth of the proposition or the belief in the proposition. While in a solution searching process, excitedness describes the ability and/or desire to solve the problem. By introducing simple flows and their network graphs, the process of excitedness flows on the network is described be a set of differential equations with steady state solutions and stability analysis performed by applying Markov process theory. By introducing the concepts of complex flows and multi-branch graphs, the process of excitedness flows on the graph is also described by a set of differential equations with steady state solutions and stability analysis performed similar to Prigogine's theory of dissipative structures.1 Finally, the idea of using computers in netlike inference is proposed.

Movement and Time: Exertion and Perceived Duration

This study examined differences in consciousness indexes (perceived duration of time) at different levels of physical exertion within the framework of Newman's model of health and with emphasis on Prigogine's theory of dissipative structures. The sample consisted of 100 volunteers participating in regular aerobic exercise. Instruments included 817E Monarch Stationary Bicycles, 1800 Dynamap Automatic Blood Pressure/Pulse Monitors, the production method of time estimation, and the Perceived Exertion Scale. Repeated measures ANOVA revealed significant differences in consciousness indexes during exertion (p less than .00001). Paired t-tests yielded significant differences between the resting consciousness index and consciousness indexes at preferred, increased, and decreased exertion levels (p = .000). Results indicate that the consciousness index decreased with physical exertion regardless of actual exertion level. In addition, changes in perceived exertion and in physiological parameters suggest a pattern of expanding consciousness that is consistent with the theoretical framework.

Modeling Suburbanization as an Evolutionary System Dynamic

The research undertaken investigates the applicability of Allen and Sanglier's dynamic model of urban system evolution to the process of suburbanization occurring in the post‐World War II United States. The model, derived from principles of the theory of dissipative structures formulated by Ilya Prigogine, considers the urban system as open and far from equilibrium, thereby allowing a dynamic evolution which has the following properties. The structure of a system at any point in its development is historically contingent upon the sequence of structures it has exhibited in its past, and on the precise nature of random fluctuations which have acted to induce structural change. The joint action of chance and determinism influence a system's evolution through the complex interactions and feedback mechanisms embedded in its structure. The critical point at which these forces cause the system to undergo a structural change is called a bifurcation point. The model allows that the microdynamics of the system underlie its macrostate. This implies, therefore, the opportunity for individuals to influence the system's structure and for the possibility for creative system evolution to occur.The central question of the research was whether the processes of deconcentration of population and dispersal of employment from the central cities to the suburbs of large U.S. metropolises, with the resulting morphological shifts from mono‐ to polycentric urban forms, represent structural changes of the sort defined and modeled by Allen and Sanglier's adaptation of Prigogine's theory. The introduction of a calibration procedure, unspecified in previous applications of the model, provides a means whereby the calibration of the many system parameters can proceed in a systematic fashion, offering insight into the function of these parameters in the overall dynamic and their interactions with one another. Research results highlight the benefits of Allen and Sanglier's approach and areas inviting further investigation.

Newman's Theory of Health as Praxis

Newman presents an overview of her theory of health as expanding consciousness in the context of her odyssey for appropriate research methodology. She identifies the perspective that directs her theory and research as the evolving pattern of the whole and credits Rogers' theory of unitary human beings as providing direction for the development of this theory. Bohm's theory of implicate order, Prigogine's theory of dissipative structures, and Young's theory of human evolution are in corporated as supportive to the theory. The author advocates research as praxis and emphasizes process as content. A priori theory is central to the research aimed at recognition of the pattern of evolving conscious ness and its action potential.

Consciousness As a Dissipative Structure: An Extension of the Newman Model

Newman's model of health as the expansion of consciousness and Prigogine's theory of dissipative structures provide the framework for the development of a model of consciousness as a dissipative structure. Relationships among Type A behavior, temporal orientation, and death anxiety are examined and explicated within the human field pattern of consciousness as a dissipative structure. Type A behavior, future orientation, and death anxiety are proposed as manifestations of consciousness with the potential to evolve to higher levels in accordance with Prigogine's theory. Preliminary research findings related to the model and suggestions for future research are also presented.

Thermodynamic properties of decalins mixed with hexane isomers at 298.15 K. II. Excess volumes and isentropic compressibilities

Excess volumes V E and differences in isentropic compressibilities between the solution and the pure state, Δκ s , have been determined at 298.15 K for decalins mixed with hexane isomers. The maximum values of V E are found to correlate linearly with differences of κ s of the pure component liquids. The Δκ s results were used for further detailed discussion of V E. The experimental results are also analysed by using the Flory—Patterson—Prigogine(FPP) theory.

An explicit approach to the Λ-operator and the H-theorem in the Prigogine theory of irreversibility

Abstract A reformulation of the Prigogine theory of irreversible dynamical systems is given. In contrast to the previous works a stochastic integral with respect operator valued martingales is employed here. This approach provides a mathematically rigorous and simple construction of the Λ operator for dynamical flows. It has an explicit random character. We derive also the Boltzmann H-theorem explicitly from the properties of the semigroup only. Finally, the form of the Boltzmann kinetic equation for the irreversible dynamics is found.

Stability of stellar structure in non-equilibrium thermodynamics

The stability of a star undergoing C-N-O cycle is examined using the mean field method in Prigogine's theory of non-equilibrium thermodynamics. It is found 1) that convection and diffusion in the energy-generating zone have an important effect on the stability and 2) that the star is stable if the velocity divergence is less than the diffusion coefficient, or, equivalently, the temperature fluctuation is less than a certain value.

Coherence in Disordered Condensed Matter. II: Size of Coherent Structures in Condensed Systems owing to Luminescent Transitions, and Detection of D‐Fluctuations

AbstractA connection between complex scaling method (CSM), the Prigogine theory of star‐unitary transformations and the luminescence spectroscopic experiment is presented. CSM predicts the existence of coherent (or: dissipative) structures appearing spontaneously in amorphous matter like liquids, due to the thermal motion. A typical spatial size of these coherent structures is estimated. The connection with measurements of D‐fluctuations is shortly discussed.

The role of stable manifolds and information in the Prigogine theory of irreversibility

The image of Dirac measures τx by the operator Λ of the construction of Prigogine and collaborators is shown to be concentrated in the stable manifold Xst(x) and its density function ρ is studied for Bernoulli shifts. The valuev∞ = exp[−hμ(T)], wherehμ(T) is the Kolmogorov entropy, appears as a critical point for the behavior of ρ. It is also proved that no loss of information is involved by passing from the dynamical system to the Markov process when vx > 1/2. The discussion is based on the introduction of an invariant for Markov systems that generalizes the usual Kolmogorov entropy for dynamical systems.

Prandtl Number Effect on Be´nard Convection in Porous Media

A numerical study of buoyancy-driven two-dimensional convection in a fluid-saturated horizontal porous layer is reported emphasizing the nonlinear inertial effect on heat transport. The Forchheimer–Brinkman–Darcy–Boussinesq formulation and a single energy equation for the volume-average temperature are used. Closure to the wavenumber selection problem is sought through a criterion based on the Glansdorff and Prigogine theory of nonequilibrium thermodynamics. Good agreement with laboratory data and the analogy with the Rayleigh–Be´nard problem are corroborative facts which justify similar non-Darcian formulations and demonstrate the role of the quadratic inertial terms in decreasing the mean convective heat transfer across the layer.

Total and preferential sorption in polar ternary systems

In this paper we have applied the Flory–Huggins and Flory–Prigogine theories to several polar ternary systems of the type polymer–liquid 1–liquid 2. From light scattering and viscosity measurements we have calculated several experimental parameters necessary to calculate the total sorption function, Y, and preferential sorption coefficient, λ.

A possible physical interpretation of the Λ operator in the prigogine theory of irreversibility

We argue that if observations take a finite time Λ t and if one can only distinguish points in phase space separated by distances greater than ϵ then the Λ operator is determined by these conditions.

From general laws to singularities.

This article comprises several sections. The first is devoted to an explanation of a number of notions stemming from work by Ilya Prigogine and others on open systems far from equilibrium. As a result of this work, I have been able to stand back from the traditional approach employed in family therapy, that of open systems at equilibrium (the theory of Ludwig von Bertalanffy). The second section describes a clinical example based on elements close to Prigogine's theories. In the third part I develop an approach that--although continuing to draw on Prigogine's work--is much more closely linked to the research I have carried out with Félix Guattari over recent years. In this part I attempt to study a level that, in my view, has too often been left outside the field of inquiry: that of couplings between "singularities" of members of the family system and the therapist. A clinical case is presented in which this "semiotic" level, as Guattari terms it, is used together with that of the "intrinsic rules" of the system. Finally, I propose a few avenues of inquiry and research on the basis of the concepts presented.

Time Operator, D‐Fluctuations, and Microscopic Irreversibility in Spectroscopic Processes

AbstractPrigogine has emphasized that there is a “degeneracy” in quantum theory, where the Hamiltonian plays a dual role as (a) the generator of time evolution and (b) the energy observable. This prevents the exact treatment of irreversible phenomena on the microscopic quantum mechanical level. The removal of the aforementioned degeneracy can be achieved with the aid of a star‐unitary similarity transformation depending explicitly on the star‐Hermitian operator of the “intrinsic time”. Its physical significance is shown in the context of luminescence spectroscopy, where a novel kind of (dynamically induced or D‐) fluctuations around steady photoemission states is predicted. A photon counting/spectroscopic experiment has been performed which permits to detect D‐fluctuations and, at the same time, allows us to resolve broad spectroscopic bands by detection of the underlying finer “pure” vibronic transitions. The experimental findings clearly show the physical significance of Prigogine's Microscopic Theory.

Generalization of Fröhlich's thermodynamic model of the living state phase transition

Based on some experimental evidence for the existence of metastable ferroelectric phases in living substances Fröhlich proposed a simple thermodynamic description of the living state. The free energy of a cell is written as a polynomial in the total electric polarization and the macroscopic deformation. The two variables are coupled which allows for piezoelectric effects. Haken argued that the transition to the living state is a field-induced phase transition and Fröhlich included the presence of large electric fields as a prerequisite for the biological coherence. Therefore, the thermodynamic formulation requires an additional term representing interactions with an external electric field. We analyze a generalized model free energy and arrive at results which confirm earlier predictions. Above a threshold field a ferroelectric phase can be established which remains stable even after the field has been removed. In conclusion, a possible further generalization of the model to embrace time dependence and spatial inhomogeneities is sketched. It appears that a link with Prigogine's theory of dissipative structure can be traced.