Some properties of stochastic equations for coupled chemical reactions far from equilibrium

Solutions of master equations for coupled chemical reactions far from equilibrium with one varying molecule species are studied and used for getting information about nonlinear Fokker-Planck equations and slow time-dependent processes such as extinction to an absorbing state and transition between several steady states. The Fokker-Planck equation solution is compared to that of the master equation in a relative sense and it is shown that they agree quite well in some important situations but that in general the cases can deviate considerably, when, e.g., accounting for the mutual importance of two probability maxima.     

Time-dependent probability density of statistical mechanics

We study fluctuations around nonequilibrium steady states of some model nonlinear chemical systems. A previous result of Nicolis and Prigogine states that the mean square fluctuation computed from a master equation in the space of internal states of the reacting species is identical to that calculated from Einstein's fluctuation formula. Our analysis of fluctuations based on that master equation leads with the assumption of local equilibrium to a result identical to that obtained from a master equation for the total concentration of the reacting species, which is different from the equilibrium (Einstein relation) result. Nicolis and Prigogine approximated one term in their master equation, and a discussion of this approximation is presented. The master equation without this approximation yields at equilibrium the result expected on the basis of Einstein's formula.Work supported in part by the National Science Foundation and Project SQUID, Office of Naval Research.     

Intrinsic randomness and spontaneous symmetry-breaking in explosive systems

The effect of fluctuations of either thermodynamic or environmental origin on ignition in explosive systems is analyzed, with special emphasis on thermal explosion. A simple model due to Semenov is first analyzed in the zero-dimensional approximation. It is shown that the ignition times exhibit a wide dispersion, which at the level of the probability distribution of temperature shows up as a transient bimodality. Next, an extension to a spatially distributed system is developed. It is shown that fluctuations induce unexpected symmetry-breaking phenomena, reflected by a considerable dispersion of the position of the first hot spot initiated in the system.     

A statistical model for instable thermodynamical systems

A generic model is presented for statistical systems which display thermodynamic features in contrast to our everyday experience, such as infinite and negative heat capacities. Such system are instable in terms of classical equilibrium thermodynamics. Using our statistical model, we are able to investigate states of instable systems which are undefined in the framework of equilibrium thermodynamics. We show that a region of negative heat capacity in the adiabatic environment, leads to a first order like phase transition when the system is coupled to a heat reservoir. This phase transition takes place without a phase coexistence. Nevertheless, all intermediate states are stable due to fluctuations. When two instable system are brought in thermal contact, the temperature of the composed system is lower than the minimum temperature of the individual systems. Generally, the equilibrium states of instable system cannot be simply decomposed into equilibrium states of the individual systems. The properties of instable system depend on the environment, ensemble equivalence is broken.     

Particle size effect of a.c. superconducting properties in compound

Using a new starting material of Ba₂Cu₃O₅ and a three step heat treatment, single phase Tl₂Ca₁Ba₂Cu₂O₈ high- superconducting samples have been prepared, possessing the onset- and critical temperatures K and K. The morphology dependent value of is 17 Oe, 8 Oe and 5 Oe at 77 K in the case of bulk, crushed and powdered materials, respectively. The a.c. susceptibility, r.f. susceptibility and microwave absorption properties show a significant dependence on the particle size with a sharp change in the interval between 750 μm and 1200 μm. These experiments provide characteristic parameters for intergrain material (treated as 3D Josephson network) as mm, Oe and A/cm² at 77 K. The data are controlled by modulated microwave absorption measurements. The results obtained can be explained well both by the finite size junction model and cavity mode absorption model. The Josephson network is determined unambiguously by metallic S-N-S weak links. Received 10 October 1998     

Chaotic Hypothesis, Fluctuation Theorem and Singularities

The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention and can lead to apparent inconsistencies. In particular there are several cases that have been considered in the literature in which singularities are built in the models: for instance when among the forces there are Lennard-Jones potentials (which are infinite in the origin) and the constraints imposed on the system do not forbid arbitrarily close approach to the singularity even though the average kinetic energy is bounded. The situation is well understood in certain special cases in which the system is subject to Gaussian noise; here the treatment of rather general singular systems is considered and the predictions of the chaotic hypothesis for such situations are derived. The main conclusion is that the chaotic hypothesis is perfectly adequate to describe the singular physical systems we consider, ıe deterministic systems with thermostat forces acting according to Gauss' principle for the constraint of constant total kinetic energy (“isokinetic Gaussian thermostats”), close and far from equilibrium. Near equilibrium it even predicts a fluctuation relation which, in deterministic cases with more general thermostat forces (ıe not necessarily of Gaussian isokinetic nature), extends recent relations obtained in situations in which the thermostatting forces satisfy Gauss' principle. This relation agrees, where expected, with the fluctuation theorem for perfectly chaotic systems. The results are compared with some recent works in the literature. PACS: 47.52.+j, 05.45.-a, 05.70.Ln, 05.20.-y     

Mechanistic approach to generalized technical analysis of share prices and stock market indices

Classical technical analysis methods of stock evolution are recalled, i.e. the notion of moving averages and momentum indicators. The moving averages lead to define death and gold crosses, resistance and support lines. Momentum indicators lead the price trend, thus give signals before the price trend turns over. The classical technical analysis investment strategy is thereby sketched. Next, we present a generalization of these tricks drawing on physical principles, i.e. taking into account not only the price of a stock but also the volume of transactions. The latter becomes a time dependent generalized mass. The notion of pressure, acceleration and force are deduced. A generalized (kinetic) energy is easily defined. It is understood that the momentum indicators take into account the sign of the fluctuations, while the energy is geared toward the absolute value of the fluctuations. They have different patterns which are checked by searching for the crossing points of their respective moving averages. The case of IBM evolution over 1990-2000 is used for illustrations. Received 31 December 2001     

Theory for the Exciton Magnetic Polaron in Diluted Magnetic Semiconductors with Thermodynamic Fluctuations of Magnetization

The photoinduced self-trapped exciton magnetic polaron (ST-EMP) in diluted magnetic semiconductors has been the subject of intensive investigations related to the observed photoluminescence during the last two decades. The stability, however, seems still controversial. In this article we study the stability of ST-EMP theoretically, including thermodynamic fluctuations of magnetization. The calculation suggests that the EMP in CdTe(Mn) (Mn: 10-20%) is not self-trapped except at low temperatures below ¨ 1 K, but the other primary localization mechanisms, for example, alloy potential fluctuations, are necessary to the localization of EMP above ¨ 1 K.