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Master equation
About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.
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TL;DR: In this article, the modified Boltzmann Integro-differential equation for this quantity has been previously derived but so far only limited solutions of the resulting equation have been obtained.
Abstract: For molecules with degenerate internal states, the single-particle distribution function must be replaced by a density matrix, or better, if the translational motion is treated classically, by a Wigner distribution-function density matrix. The modified Boltzmann Integro-differential equation for this quantity has been previously derived but so far only limited solutions of the resulting equation have been obtained. Methods are herein discussed which enable the standard methods for the solution of the classical Boltzmann equation to be applied to the solution of this equation. Complications involving commutation properties are resolved.
68 citations
TL;DR: In this article, a comparison of the Fokker-Planck equations obtained by the Ito prescription and by the Stratonovich prescription for physical systems described by a Langevin equation with non-additive fluctuations is presented.
Abstract: We present a comparison of the Fokker-Planck equations obtained by the Ito prescription and by the Stratonovich prescription for physical systems described by a Langevin equation with non-additive fluctuations. Our main conclusion is that the Stratonovich prescription is the one that should always be used to describe physical systems. This conclusion is shown to be consistent with results obtained from path integral and Master equation approaches.
68 citations
TL;DR: An on-the-fly variant of AU is presented, where the original algorithm for AU is improved at the cost of a small approximation error, and it is shown that this approach is particularly well-suited for biochemical reaction networks.
Abstract: Within systems biology there is an increasing interest in the stochastic behaviour of biochemical reaction networks An appropriate stochastic description is provided by the chemical master equation, which represents a continuous-time Markov chain (CTMC) The uniformisation technique is an efficient method to compute probability distributions of a CTMC if the number of states is manageable However, the size of a CTMC that represents a biochemical reaction network is usually far beyond what is feasible In this study, the authors present an on-the-fly variant of uniformisation, where they improve the original algorithm at the cost of a small approximation error By means of several examples, the authors show that their approach is particularly well-suited for biochemical reaction networks
67 citations
TL;DR: The waiting time distribution w(τ) as discussed by the authors, i.e., the probability for a delay τ between two subsequent transition (jumps) of particles, is a statistical tool in (quantum) transport.
Abstract: The waiting time distribution w(τ), i.e. the probability for a delay τ between two subsequent transition (‘jumps’) of particles, is a statistical tool in (quantum) transport. Using generalized Master equations for systems coupled to external particle reservoirs, one can establish relations between w(τ) and other statistical transport quantities such as the noise spectrum and the Full Counting Statistics. It turns out that w(τ) usually contains additional information on system parameters and properties such as quantum coherence, the number of internal states, or the entropy of the current channels that participate in transport.
67 citations
TL;DR: In this article, a statistical theory for the stochastic Burgers equation in the inviscid limit is developed for the probability density functions of velocity, velocity difference, and velocity gradient.
Abstract: A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference, and velocity gradient are derived. No closure assumptions are made. Instead, closure is achieved through a dimension reduction process; namely, the unclosed terms are expressed in terms of statistical quantities for the singular structures of the velocity field, here the shocks. Master equations for the environment of the shocks are further expressed in terms of the statistics of singular structures on the shocks, namely, the points of shock generation and collisions. The scaling laws of the structure functions are derived through the analysis of the master equations. Rigorous bounds on the decay of the tail probabilities for the velocity gradient are obtained using realizability constraints. We also establish that the probability density function Q() of the velocity gradient decays as jj 7=2 as !1 . c 2000 John Wiley & Sons, Inc.
67 citations