Related papers: Chemical Kinetics, Markov Chains, and the Imaginar…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance,…
This study addresses a longstanding question regarding the mathematical proof of chaotic behavior in kinetic differential equations. Following the numerous numerical and experimental results in the past 50 years, we introduce two formal…
In small systems, quantitative discrepancies between stochastic and deterministic descriptions of chemical kinetics can be significant, with their magnitude depending on the specific reaction network. Here, we study the Finke-Watzky…
The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…
The analytic solution for the kinetic description of binary reactions can be seen as the continuum version of a basic discrete iterate mapping. This fact allows a clear definition of the reaction characteristic time which takes the backward…
The master equation for the reversible reaction A+A <--> 0 is considered in Poisson representation, where it is equivalent to a Langevin equation with imaginary noise for a complex stochastic variable \phi. Such Langevin equations appear…
From a mathematical model that describes a complex chemical kinetic system of $N$ species and $M$ elementrary reactions in a rapidly stirred vessel of size $V$ as a Markov process, we show that a macroscopic chemical thermodynamics emerges…
When the entities undergoing a chemical reaction are not available simultaneously, the classical rate equation of a reaction or, alternatively for the evolution of a population, should be extended by including non-Markovian memory effects.…
The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical system (diffusion process with Langevin or Fokker-Planck equations) and its emergent discrete,…
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…
Complex biochemical pathways or regulatory enzyme kinetics can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. This discipline provides a set of tools for quantifying and understanding the…
We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully…
Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that…