Related papers: Chemical kinetics and stochastic differential equa…
The appeal of thermodynamics to problems outside physics is undeniable, as is the growing recognition of its apparent universality, yet in the absence of a rigorous formalism divorced from the peculiarities of molecular systems all attempts…
Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…
The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for…
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems it has been shown that exact and approximate quantum dynamics methods can be made dramatically…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to solve analytically. It is particularly hard to solve for…
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 present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
Plasmas in which there is a threshold for a dominant reaction to take place (such as recombination or attachment) will have particle distributions that evolve as the reaction progresses. The form of the Boltzmann collision term in such a…
Stochastic modeling of chemical reaction systems based on master equations has been an indispensable tool in physical sciences. In the long-time limit, the properties of these systems are characterized by stationary distributions of…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
Advanced observational facilities allow to trace back the chemical evolution of the Universe, on the one hand, from local objects of different ages and, secondly, by direct observations of redshifted objects. The chemical enrichment serves…
The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At non-dilute conditions, interactions among the components can give rise to coexisting…