Measuring disorder in irreversible decay processes

Flynn, Shane W.; Zhao, Helen C.; Green, Jason R.

doi:10.1063/1.4895514

Cited by 24 publications

(30 citation statements)

References 30 publications

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“…For thermally activated processes, the stability exponents of the purely periodically driven system can thus be used to predict the reaction rates without an explicit treatment of the thermal dynamics. Extensions of this work to include an explicit treatment of the noise, systems with structured solvents environments, 78,79 and systems displaying fluctuating rates, 80 are possible next steps, and ones which we are currently pursuing.…”

Section: Discussionmentioning

confidence: 99%

Chemical reactions induced by oscillating external fields in weak thermal environments

Craven

Bartsch

Hernandez

2015

The Journal of Chemical Physics

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Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead timedependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T. Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for single-mode sinusoidal driving, the stability of the timevarying transition state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R. Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous work to the case of multi-mode driving waveforms. Excellent agreement is observed between the rates predicted by stability analysis and rates obtained through numerical calculation of the reactive flux. We also show that the optimal dividing surface and the resulting reaction rate for a reactive system driven by weak thermal noise can be approximated well using the transition state geometry of the underlying deterministic system. This agreement persists as long as the thermal driving strength is less than the order of that of the periodic driving. The power of this result is its simplicity. The surprising accuracy of the time-dependent noise-free geometry for obtaining transition state theory rates in chemical reactions driven by periodic fields reveals the dynamics without requiring the cost of brute-force calculations.

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Section: Discussionmentioning

confidence: 99%

Chemical reactions induced by oscillating external fields in weak thermal environments

Craven

Bartsch

Hernandez

2015

The Journal of Chemical Physics

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“…The purpose of this paper is to investigate how these two models are affected by stochastic noise, which is now believed to be crucial in many systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For instance, variability has emerged to be a key factor in understanding the development of tumours [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Time-dependent probability density functions and information geometry in stochastic logistic and Gompertz models

2017

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A probabilistic description is essential for understanding growth processes far from equilibrium.In this paper, we compute time-dependent Probability Density Functions (PDFs) in order to investigate stochastic logistic and Gompertz models, which are two of the most popular growth models.We consider different types of short-correlated internal (multiplicative) and external (additive) stochastic noises and compare the time-dependent PDFs in the two models, elucidating the effects of the additive and multiplicative noises on the form of PDFs. We demonstrate an interesting transition from a unimodal to a bimodal PDF as the multiplicative noise increases for a fixed value of the additive noise. A much weaker (leaky) attractor in the Gompertz model leads to a significant (singular) growth of the population of a very small size. We point out the limitation of using stationary PDFs, mean value and variance in understanding statistical properties of the growth far from equilibrium, highlighting the importance of time-dependent PDFs. We further compare these two models from the perspective of information change that occurs during the growth process. Specifically, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory quantifies the total number of different states that the system undergoes in time, and is called the information length. We show that the time-evolution of the two models become more similar when measured in units of the information length and point out the merit of using the information length in unifying and understanding the dynamic evolution of different growth processes.

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“…Comparing the inequality for first-order kinetics 29 to that of higher-order kinetics, we see the inequalities are related:…”

Section: B Inequality For Disorder In Irreversible Kineticsmentioning

confidence: 99%

“…The representation of J n and L n we define above is just one from our earlier work on first-order (n = 1) rate processes, 29 which established a connection between the rate coefficient and a modified Fisher information.…”

Section: 31mentioning

confidence: 99%

Order and disorder in irreversible decay processes

Nichols

Flynn

Green

2015

The Journal of Chemical Physics

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Dynamical disorder motivates fluctuating rate coefficients in phenomenological, mass-action rate equations. The reaction order in these rate equations is the fixed exponent controlling the dependence of the rate on the number of species. Here we clarify the relationship between these notions of (dis)order in irreversible decay, n A → B, n = 1, 2, 3, . . ., by extending a theoretical measure of fluctuations in the rate coefficient. The measure, J n − L 2 n ≥ 0, is the magnitude of the inequality between J n , the time-integrated square of the rate coefficient multiplied by the time interval of interest, and L 2 n , the square of the time-integrated rate coefficient. Applying the inequality to empirical models for non-exponential relaxation, we demonstrate that it quantifies the cumulative deviation in a rate coefficient from a constant, and so the degree of dynamical disorder. The equality is a bound satisfied by traditional kinetics where a single rate constant is sufficient. For these models, we show how increasing the reaction order can increase or decrease dynamical disorder and how, in either case, the inequality J n − L 2 n ≥ 0 can indicate the ability to deduce the reaction order in dynamically disordered kinetics.

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Measuring disorder in irreversible decay processes

Cited by 24 publications

References 30 publications

Chemical reactions induced by oscillating external fields in weak thermal environments

Chemical reactions induced by oscillating external fields in weak thermal environments

Time-dependent probability density functions and information geometry in stochastic logistic and Gompertz models

Order and disorder in irreversible decay processes

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