Evolution Of Open System Research Articles

Quantum state diffusion, localization and quantum dispersion entropy

The quantum state diffusion model introduced in an earlier paper represents the evolution of an individual open quantum system by an Ito diffusion equation for its quantum state. The diffusion and drift terms in this equation are derived from interaction with the environment. In this paper two localization theorems are proved. The dispersion entropy theorem shows that under special conditions, which are commonly satisfied to a good approximation, the mean quantum dispersion entropy, which measures the mean dispersion or delocalization of the quantum states, decreases at a rate equal to a weighted sum of effective interaction rates, so that the localization always increases in the mean, except when the effective interaction with the environment is zero. The general localization theorem provides a formula for more general conditions.

The quantum state diffusion picture of physical processes

In earlier papers the authors introduced a quantum state diffusion model for the evolution of an individual open quantum system and proved localization theorems based on this model. This paper shows in more detail how the diffusion leads to localization in position and phase space, and to symmetry breaking for chiral molecules. The theory of radioactive decay of absorbers and detectors is described in the state diffusion picture. The Mott and Gurney theory of latent image formation in photography is presented in its state diffusion version. It is an example of quantum detection without significant amplification.

238U/ 204Pb in MORB and open system evolution of the depleted mantle

Concentrations of U, Th and Pb were determined by isotope dilution on 30 mid-ocean ridge basalt (MORB) glasses. The mean values of 238U/ 204Pb (μ) and 232Th/ 238U (κ) in these glasses are 11.20 and 2.67 respectively. There are significant differences in these ratios between ocean basins. Mean κ values increase in the order Atlantic < Pacific < Indian; mean μ is higher in Pacific MORB than in Indian and Atlantic MORB, but differences between the Atlantic and Indian are not significant. μ correlates strongly with U concentration, but not with Pb concentration or with 206Pb/ 204Pb . The correlation of μ with U but not with 206Pb/ 204Pb reflects the effect of partial melting and fractional crystallization on μ. Since the maximum value of U in the depleted mantle must be less than the bulk silicate earth value of 0.018 ppm, the μ-U correlation can be used to estimate the maximum mean value of μ in the depleted mantle ( μ DM ). This yields a maximum μ DM of 4.67. Similarly, the correlation between μ and Rb/Sr suggests a maximum μ DM of 6.3. These results are consistent with values for μ DM derived using mass balance from the crustal and depleted mantle values of κ, the depleted mantle Pb/Ce ratio, and the crustal abundance of Ce. The value of μ DM thus seems to be less than the bulk earth value, estimated to be 8 ± 2. This is consistent with the incompatible-element-depleted character of this reservoir, but inconsistent with Pb isotope ratios, which record time-integrated values for μ of 8–9, and which indicate that μ has increased over time. This inconsistency requires that the depleted mantle be an open system with a residence time for Pb of 1 ± 0.5 Ga. Neither the continental crust nor a primitive lower mantle have the appropriate isotopic composition to be the source of Pb in the depleted mantle. Mantle plumes do have the appropriate isotopic composition, and as little as 10% of the observed plume flux is needed to mix with the depleted mantle to supply the required flux of Pb.

On evolution of open dynamical systems: Some algebraic methods

Open dynamical systems which are governed by a finite number of ordinary differential equations with controls (time-dependent control parameters) constitute a large and important class of models for practical purposes. In the last few years, there has been considerable interest and progress in algebraic methods for solving the equations of the form $$\dot x\left( t \right) = L_0 x\left( t \right) + \sum\limits_{j = 1}^r {u\left( t \right)L_i x\left( t \right)} ,$$ i.e. bilinear models. In this paper, intended as an expository introduction to the main results of system-theoretic approach to the modelling of open systems, a new polynomial representation of solutions to (*) is discussed.

The adaptation of Pearce element ratio diagrams to complex high silica systems

Pearce element ratios (PERs, of Pearce 1968) express geochemical data in a form where variations in absolute compositions of an igneous suite can be evaluated. Generally the denominator value in the ratio is taken as a major element abundance, but it is argued here that Zr provides a more suitable choice. Zr remains incompatible in magmatic systems up to ≈68 wt.% SiO2 because zircon fractionation can be suppressed by high melt temperatures and increased volatile contents. The use of Zr thus permits PER modelling to be extended to much higher levels of silica than previously investigated. However, such systems are more complex than those just involving simple basaltic magmas. Besides fractionation, the processes of magma mixing, combined assimilation and fractional crystallization, and the initial degree of partial melting in the mantle source must also be considered. To distinguish and evaluate these processes a set of example suites are investigated from a complex synextensional calc-alkaline province in the western USA. Samples within most individual suites can be modelled by fractionation, however a significant trend orthogonal to the main fractionation vector is also apparent, and open system processes are inferred. Successful modelling is achieved on an inter-suite basis using diagrams with axis functions of ([4(Ca+Na)+0.5(Fe+Mg)]/Zr versus (Si+Al)/Zr). Potential open system evolution paths between mafic end members and crustal contaminants are also displayed and evaluated on these same diagrams. The encouraging results suggest that such PER diagrams may be employed as a versatile tool for investigating the systematics of related igneous suites over a wide area.

The weak coupling limit as a quantum functional central limit

We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.

Open-system evolution versus source control in basaltic magmas: Matachewan–Hearst dike swarm, Superior Province, Canada

The 2.45 Ga Matachewan–Hearst dike swarm was emplaced over 250 000 km2 in diverse granitoid–greenstone and metasedimentary terranes of the Superior Province of Canada. The Fe-rich tholeiitic dikes host large, uniform plagioclase megacrysts and display significant trace-element variations, e.g., (La/Sm)N = 0.62–2.23, not correlated to terrane lithologies.Fractional crystallization alone cannot produce these variations or simultaneously account for both major- and trace-element abundances. Combined periodic replenishment–fractional crystallization (RFC) in shallow magma chambers is consistent with major- and trace-element concentrations and with field evidence for periodic magma injection within the dikes. RFC cannot, however, produce the observed variation in incompatible-trace-element ratios, e.g., (La/Sm)N. Models invoking mixed mantle sources are unsuccessful at reproducing trace-element trends. Combined assimilation–fractional crystallization (AFC) models, assuming depleted parental magmas and using crustal rock data from xenoliths and from the Kapuskasing Structural Zone, can accommodate the trace-element variations, including the light-rare-earth-element enrichment and the observed relative depletions of the high-field-strength elements. The AFC process apparently took place in the lower crustal regions from where evolved magmas were periodically transported to shallow chambers dominated by RFC.

The origin and evolution of magmas from the San Pedro-Pellado volcanic complex, S. Chile: multicomponent sources and open system evolution

The San Pedro-Pellado volcanic complex is located at 36° S in the Chilean Andes. The eruptive rocks of the complex record the development and collapse of a caldera, followed by voluminous, largely basaltic andesite, volcanism. At each stage of evolution, crystal fractionation was accompanied by variable degrees of contamination and mixing. Large variations in incompatible element ratios cannot be produced by closed system evolution. Correlations between indices of differentiation and incompatible element ratios, together with high δ 18O values, indicate that basaltic andesites have assimilated crust to generate the evolved volcanic rocks at San Pedro-Pellado. Even in the most mafic rocks, however, incompatible element characteristics are variable as a result of source heterogeneity and deep level processes. The restricted ranges in isotope ratios of Sr, Nd and Pb among San Pedro-Pellado rocks are due to the small contrast in isotopic compositions between magma and wallrock. Three source components are recognized as contributing to parental magmas at San Pedro-Pellado. Although the relative contributions of each cannot be quantified, the volumetrically dominant source component is the sub-arc asthenospheric mantle (MORB source). The major source of LILE is thought to be slab-derived fluids which modified the sub-arc mantle. Other incompatible elements may also have been enriched by interaction with the continental lithosphere (mantle and/or lower crust) during ascent.

Evolutionary Cybernetic Systems Theory Considered as a Chapter of General Systems Theory — A Viewpoint

The approach is based on an evolutionary interpretation of the fundamental concepts of cybernetics, general systems theory, information theory, theory of automata, autopoiesis, etc. In the author's view, this enables us to formulate principles of the evolutionary theory of cybernetic systems which is visualised as the theory of structures, functions and evolution of cybernetic or control systems. This suggests a heuristic idea of cybernetic evolution as the higher stage of negentropic universal evolution of open systems.

129I/ 127I variations among enstatite chondrites

This paper presents the 129I/ 127I composition for 11 different enstatite chondrites. There is a well-defined hiatus in iodine isotopic compositions separating the enstatite chondrites. The hiatus correlates with a similar hiatus defined by variations in chemical composition (both major and minor elements). EH(4,5) chondrites have 129I/ 127I ratios ∼20% higher (∼ 4 m.y. older) than EL(6) chondrites. The enstatite chondrites are the third meteorite group, joining silicates in IAB irons and C3V carbonaceous chondrites, in which 129I/ 127I correlates with chemical composition. Within each enstatite chondrite group, the variations in initial iodine isotopic composition is less than ~ ±4%, comparable to the experimental resolution. The ~20% difference between EH and EL may indicate a maximum iodine isotopic heterogeneity between the EH and EL nebular reservoirs. Alternatively, if EH and EL chondrites evolved from a homogeneous iodine isotopic reservoir, then the EL group must have evolved ~ 4.0 m.y. longer than the EH group and either in an environment with a much lower I/Xe ratio than presently observed or one which was open to the loss of radiogenic 129Xe. The latter case may imply a nebular environment and would therefore be consistent with the open system evolution required to produce the chemical hiatus. The duration of subsequent evolution in the high I/Xe environment must have been ≲1 m.y. and probably represents thermal metamorphism in two different parent bodies.

Open System Magmatic Evolution of the Taos Plateau Volcanic Field, Northern New Mexico: II. The Genesis of Cryptic Hybrids

Tholeiitic lavas of the Servilleta Basalt exhibit only subtle textural and mineralogical evidence for a hybrid origin, but elemental and isotopic analyses of these basalts are best modeled in terms of mixing Servilleta parent magma with a range of contemporaneous andesite and dacite magmas. Cryptic compositional heterogeneities in some flows interpreted as hybrids apparently reflect incomplete homogenization following pre-emptive magma mingling. The general scarcity of mixing-related textural disequilibrium is ascribed in part to mixing of mineralogically similar end-members. Eradication of some phenocrysts during post-mixing residence and evolution in a convecting magma body may be an even more important factor. Eruptions of hybrid magmas may frequently be triggered by magma mixing events (i.e. injection or replenishment), and mingling of compositionally diverse magmas may ensue as a consequence of tapping a compositionally graded or layered magma chamber. These hybrids are instantly recognizable by the preservation of disequilibrium textures and mineral assemblages, and by discontinuous compositional heterogeneities. Cryptic hybrids, which have not preserved this record, will be recognizable as mixed magmas primarily by geochemical evidence for open system evolution.

The origin of adaptation and dyssymmetry in the evolution of autocatalytic systems

The evolution of open systems that include several autocatalytic processes in parallel or in series is mathematically analyzed. For the case of two reactions in parallel, such systems progressively and finally select the reaction pathway which involves the better autocatalyst. The effect of parameters influencing the rate of this evolution is discussed. Where catalysts are strictly equivalent, e.g. enantiomers in a symmetrical surrounding, the evolution is amplified by fluctuations and retains finally only one reaction pathway, if the autocatalytic rates of reactions are more than proportional to the catalyst concentrations. When including two reactions in series, these open systems are also able to give oscillations.

The averaging method for asymptotic evolutions. II. Quantum open systems

The method of averaging is applied to study the reduced evolution of a quantum open system. Successive approximate evolutions are derived, and they are shown to be asymptotic to the exact evolution of the open system, under conditions which are satisfied in the case of a system coupled to a quasi-free reservoir, whose correlation functions are exponentially descreasing in time.

Theory of Ostwald ripening for open systems

Diffusion-controlled coarsening (Ostwald ripening) of a precipitate is analyzed for the case of an open system, immersed in a reservoir of constant solute concentration. Equivalence of the evolution of such open systems and closed systems studied previously is established in the limit of infinite systems. The cause of this equivalence is screening of the bulk of the system from the reservoir by diffusive interactions between the precipitated particles. The applicability to large, but finite systems is discussed.

Isotopic constraints on open system evolution of the Laacher See magma chamber (Eifel, West Germany)

The Laacher See phonolite tephra sequence (11,000 years B.P.) of the Quaternary East Eifel volcanic field (West Germany) represents an inverted, chemically zoned magma column. Mafic and differentiated phonolites, respectively, represent the lowermost and uppermost erupted portion of the Laacher See magma chamber. Sr and Nd isotopic compositions of whole rocks, matrices and phenocrysts have been analyzed in order to provide constraints for open versus closed system evolution of the Laacher See magma chamber. 87Sr/ 86Sr isotope ratios of mafic phonolites and their phenocrysts are slightly more radiogenic than parental East Eifel basanite magmas. Bulk rock samples show a drastic increase in 87Sr/ 86Sr from mafic towards the most differentiated compositions that were erupted from the top of the magma chamber. Glass matrix separates show a parallel, but less pronounced, increase in 87Sr/ 86Sr . Phenocrysts, in contrast, show a narrow range in 87Sr/ 86Sr with a slight, but significant, increase towards the top of the magma chamber. Phenocrysts from the uppermost portion of the magma column were not in isotopic (or chemical) equilibrium with their host matrices. 143Nd/ 144Nd isotope ratios for whole rocks, matrices, and phenocrysts fall within a restricted range similar to that of East Eifel mafic magmas. A representative suite of crustal rocks (lower crustal granulites, quartzo-feldspathic gneisses, mica schists, Devonian slates and graywacke) was also analyzed in order to permit an evaluation of possible assimilation models. Our results are consistent with chemical evolution of the zoned Laacher See magma chamber mainly through crystal fractionation accompanied by minor amounts of assimilation. Slight contamination of the magma system may have involved (a) the assimilation of gneisses (?) and mica schists during the initial stage of magma chamber evolution (basanite-mafic phonolite), (b) combined assimilation-fractional crystallization (AFC) concurrent with the second differentiation stage (mafic phonolite-zoned phonolite), and (c) post-crystallization assimilation of the most fractionated volatile-rich melts of the top magma layers during a late, liquid-state (?) differentiation stage. The latter possibly involved fluid transport and/or exchange with the surrounding (partially molten) country rocks. Open system evolution of the Laacher See magma chamber is further indicated by magma mixing, as confirmed by our isotope data, leakage of volatiles from the cupola and metasomatism of wall rocks.

Stochastic models for the evolution of open stellar systems

view Abstract Citations (10) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Stochastic models for the evolution of open stellar systems Ferrini, F. ; Marchesoni, F. Abstract The authors explore the effects of stochastic processes in a one-zone model galaxy by introducing a noise term in two- and three-phase models (gas, clouds, stars). They show that in the scheme both deterministic and noise-induced phase-transition phenomena arise. The equilibrium states and the dynamical evolution of each phase are influenced greatly. The authors solve some simplified cases analytically and check the results through numerical simulations. Publication: The Astrophysical Journal Pub Date: December 1984 DOI: 10.1086/162659 Bibcode: 1984ApJ...287...17F Keywords: Astronomical Models; Computational Astrophysics; Galactic Evolution; Galactic Structure; Stellar Evolution; Stellar Systems; Stochastic Processes; Computerized Simulation; Phase Transformations; Random Noise; Stellar Models; Astrophysics full text sources ADS |

Unscrambling the lead model ages

A linear relation is derived for the secular evolution of 206 Pb 204 Pb , 207 Pb 204 Pb and 208 Pb 204 Pb ratios, that permits tests to be made for open system evolution on each system independently. Application of the method to conformable ore bodies of various geological age indicates that the available data do not demand an open system evolution for the last 3.8 b.y. 238 U 204 Pb and 232 Th 204 Pb of 9.66 ± 0.15 and 37.65 ± 1.14 respectively fit best the data for this time interval. A single stage evolution since 4.5 b.y. is unlikely, however, and the major events of continent formation postdate the Earth accretion by at least 400 m.y. The larger scatter of 207 Pb 204 Pb data about the evolution line relative to the other isotopic ratios is also interpreted as resulting from a series of continental differentiation events taking place at 3.85 ± 0.15 b.y.

The averaging method for asymptotic evolutions. I. Stochastic differential equations

Asymptotic evolutions of open systems are studied. Conditions are given under which successive approximate evolutions obtained by the method of averaging are asymptotic to the exact evolution of the open system. It is shown that these conditions are satisfied in the case of stochastic differential equations which describe the evolution of spins in random magnetic fields.

A simple model for examining mixing of pumped stationary states

The oxidation of cerous ion by bromate has been approximated by four irreversible bimolecular processes. When this mechanism is modeled numerically in a continuously stirred tank reactor (CSTR), wide ranges of conditions generate two different stationary states that are stable indefinitely for identical values of the pumping parameters. By simultaneous variation of the residence time and reactant input, it is possible to move from one to the other of these states without any discontinuity in stationary state composition. If equal volumes of the two states are mixed while pumping is continued, one or the other will become dominant. The value of the residence time generating states of equal ’’dynamic stability’’ is grossly different whether the mixing is performed instantaneously by removing a barrier between those states or gradually by increasing sizes of holes in that barrier. Because relative ’’dynamic stability’’ is extremely dependent upon path even for a process as a simple as ’’ mixing’’, it appears doubtful that useful state functions can be developed to predict the direction of evolution of open systems pumped far from equilibrium.

Properties of quantum Markovian master equations

In this paper we give an essentially self-contained account of some general structural properties of the dynamics of quantum open Markovian systems. We review some recent results regarding the problem of the classification of quantum Markovian master equations and the limiting conditions under which the dynamical evolution of a quantum open system obeys an exact semigroup law (weak coupling limit and singular coupling limit). We discuss a general form of quantum detailed balance and its relation to thermal relaxation and to microreversibility.