Master equation

About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.

The complex chemical Langevin equation

Abstract: The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE’s main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE’s predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE’s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the “complex CLE” predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.

Nonequilibrium Effects in the Kinetics of Isomerization Reactions and in the Kinetics of Dissociation and Recombination of Diatomic Molecules

Abstract: A study was made of the time evolution of a system of diatomic molecules undergoing dissociation and recombination and of a system of molecules undergoing isomerization. The starting point in each case was a master equation. The particular aims of the study were to determine the conditions under which the time evolution is describable by the appropriate phenomenological equation [Eq. (1) or (2)] and also to determine whether or not the phenomenological equations can hold under far from equilibrium conditions with forward and reverse rate constants whose ratio is not the equilibrium constant. In the isomerization it was found that the appropriate phenomenological equation [Eq. (2)] always holds after a sufficiently long time. In dissociation—recombination there exist systems in which the appropriate phenomenological equation [Eq. (1)] never holds. Certain necessary conditions involving rate constants for the elementary processes and the atom concentration must be fulfilled in order for this equation to ever hold. In both dissociation—recombination and isomerization the ratio of forward and reverse rate constants is always equal to the equilibrium constant when the phenomenological equations hold.

Decoherence and thermalization.

Abstract: We present a rigorous analysis of the phenomenon of decoherence for general N-level systems coupled to reservoirs of free massless bosonic fields. We apply our general results to the specific case of the qubit. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.