Temporal asymmetry of fluctuations in nonequilibrium steady states

Temporal asymmetries of fluctuation paths in nonequilibrium microscopic shearing systems are observed for the first time. Inspired by theories that predict asymmetry of fluctuation paths in stochastic dynamics, we focus on deterministic reversible particle models, which represent a small part of a macroscopic system. We have monitored and measured the asymmetry of the fluctuation paths of various observables as they go away from and towards the mean. The understanding of such asymmetries may scatter light on how irreversibility emerges from the microscopic reversible dynamics and on the behavior of mesoscopic (nanoscale) systems.     

Temporal correlation functions of concentration fluctuations: an anomalous case

We calculate, within the framework of the continuous time random walk (CTRW) model, multiparticle temporal correlation functions of concentration fluctuations (CCF) in systems that display anomalous subdiffusion. The subdiffusion stems from the nonstationary nature of the CTRW waiting times, which also lead to aging and ergodicity breaking. Due to aging, a system of diffusing particles tends to slow down as time progresses, and therefore, the temporal correlation functions strongly depend on the initial time of measurement. As a consequence, time averages of the CCF differ from ensemble averages, displaying therefore ergodicity breaking. We provide a simple example that demonstrates the difference between these two averages, a difference that might be amenable to experimental tests. We focus on the case of ensemble averaging and assume that the preparation time of the system coincides with the starting time of the measurement. Our analytical calculations are supported by computer simulations based on the CTRW model.     

Analysis of fluctuations in chemical reactions with several steady states

The effect of fluctuations in nonequilibrium systems is treated in terms of the stochastic theory. A solution of the fundamental equation is analyzed using the Monte-Carlo method /1, 2/. The results are compared with the conclusions following from the equations corresponding to a phenomenological model.

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Open-system nonequilibrium steady state: statistical thermodynamics, fluctuations, and chemical oscillations

Gibbsian equilibrium statistical thermodynamics is the theoretical foundation for isothermal, closed chemical, and biochemical reaction systems. This theory, however, is not applicable to most biochemical reactions in living cells, which exhibit a range of interesting phenomena such as free energy transduction, temporal and spatial complexity, and kinetic proofreading. In this article, a nonequilibrium statistical thermodynamic theory based on stochastic kinetics is introduced, mainly through a series of examples: single-molecule enzyme kinetics, nonlinear chemical oscillation, molecular motor, biochemical switch, and specificity amplification. The case studies illustrate an emerging theory for the isothermal nonequilibrium steady state of open systems.     

Multiple steady states in a CSTR with total condenser: Comparison of equilibrium and nonequilibrium models

Comparison of equilibrium and nonequilibrium models of a CSTR with total condenser focused on the multiple steady states and dynamic behaviour was carried out. The steady-state behaviour of the model system, MTBE synthesis from methanol and isobutene in a reactive distillation column, was studied in terms of the input parameters, i. e. feed flow rate of methanol or butenes, reflux ratio, and mass of catalyst. The dynamic behaviour of the system during the start-up was investigated and perturbations of manipulated variables were found to cause transitions between the parallel steady states. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Sensitivity amplification in the phosphorylation-dephosphorylation cycle: nonequilibrium steady states, chemical master equation, and temporal cooperativity

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105, 585 (2003); Annu. Rev. Phys. Chem. 58, 113 (2007)] emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential DeltaG=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in PdPC, respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants," which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule that cannot be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein that can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.     

All-forward semiclassical simulations of nonlinear response functions

We propose a quantum trajectory algorithm for computing nonlinear response functions of condensed phase molecular systems based on a time-ordered expansion of the density matrix. The nth-order response function is expressed as a sum of 2(n) impulsive response pathways representing trajectories involving zero, one, and up to n interactions with short external pulses. These are evaluated using a forward propagation algorithm based upon a Liouville space extension of the Bohmian propagation method.     

Evaluation of nonlinear quantum time correlation functions within the centroid dynamics formulation

A method to evaluate nonlinear centroid correlation functions is presented that is amenable to simple numerical computation. It can be implemented with the centroid molecular dynamics method for approximate quantum dynamics with no additional assumptions. Two nonlinear correlation functions are evaluated for a model potential using this scheme and compared with results from exact quantum calculations.     

Multiplicity of steady states in oxidative heterogeneous catalysis

Typical mechanisms of heterogeneous catalytic reactions and their kinetíc models that are characterized by a plurality of steady states are considered. Models of adsorption that lead to a plurality of equilibrium adsorption states are discussed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 4, pp. 285–300, July–August, 1992.     

Dynamics of chemical reactions and nonphysical steady states

Data on the position of nonphysical (lying beyond the region of determination) steady states are shown to be of use for understanding the dynamic behavior of chemical reactions, in particular, the reasons for slow relaxations.

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Positions of steady states in two-component chemical systems

The general kinetic equation for two-component chemical systems is analyzed. It is shown that the positions of steady states in concentration spaces can be detected by a qualitative analysis of the chemical mechanism.

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Density dependences of long-range fluctuations and short-range correlation lengths of CHF3 and CH2F2 in supercritical states

Small-angle x-ray scattering (SAXS) measurements are carried out for supercritical polar fluorocarbons, CHF3 and CH2F2, along the isotherm of 1.04 in reduced temperatures with the density range from 0.3 to 1.5 in reduced units. A novel apparatus for determination of absorption factors of the sample fluids is used in the present measurements. The apparatus enables us to detect simultaneously the accurate factors during the observation of the SAXS signals. Long-range fluctuations such as density fluctuations and correlation lengths are evaluated from the obtained SAXS data. The reduced correlation lengths are obtained by normalization by each molecular size, in order to discuss the fluctuations independent of the difference of the individual molecular size. The density fluctuations and the reduced correlation lengths of CHF3 and CH2F2 are compared with those of CO2 and H2O. The results are as follows: H2O>CH2F2>CHF3 approximately CO2 in the order of magnitude. The fluctuations of CH2F2 are significantly distinguishable from those of CHF3 and show intermediate aspect between H2O and a group of CO2 and CHF3. In addition, the short-range correlation lengths, i.e., the Ornstein-Zernike direct correlation lengths, are firstly discussed from both viewpoints of density and substance dependences. The reduced short-range correlation lengths normalized by individual molecular size are found to trace a universal curve as a function of the reduced density.     

The mechanism of activation and nonequilibrium distribution functions in unimolecular reactions

Nonequilibrium distribution functions for polyatomic molecules undergoing unimolecular reaction are considered. Two limiting cases of activation by collision are investigated: the mechanism of strong impacts, in which each collision with an activated molecule may be regarded as bringing about deactivation; and the diffusion mechanism in which the transition between states is described by the Fokker-Planck equation. An accurate solution of the diffusion equation for the thermal decomposition of a nonlinear triatomic molecule makes it possible to elucidate the kinetics of various reactions in relation to the activation mechansim.     

Dynamic properties of a heterogeneous catalytic reaction with several steady states

For the simplest catalytic mechanism (three-stage) permitting several steady states of the surface, a qualitative analysis of the properties of its kinetic model trajectories has been performed. Types of the steady states have been determined. Absence of oscillations (damped and undamped) has been shown.

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Для простейшего каталитического механизма (трехстадийного), допускающего несколько стационарных состояний поверхности, проведен качественный анализ свойств траекторий его кинетической модели. Определены типы стационарных состояний. Показано отсутствие осцилляций (затухающих и незатухающих).

     

Limiting phenomena and multiplicity of steady states in gas-phase oxidation processes

It was found that in a chain-branching oxidation reaction of hydrogen at low pressures, there is a concentration range of the reagents over which there are three steady states: the boundaries of this range determine the positions of the limiting transitions between the regions of slow and rapid occurrence of the process. The dependences of the position of the limiting transitions in noncatalytic oxidation reactions of hydrogen and of oxidation of CO on platinum metals on the rate constants of the elementary stages of these processes have been compared. At different ratios of the rate constants of the heterogeneous-homogeneous catalytic process, the dependences of the reaction rate on the concentration of the reagent may contain a break, or may have the form of a loop or hystereses, both clockwise and counterclockwise.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 1, pp. 28–33, January–February, 1987.