Related papers: Optimal Fluctuations for Nonlinear Chemical Reacti…
In the last few decades, noise-induced large fluctuations and transition phenomena have garnered significant attention in a variety of scientific contexts. The concept of prehistory probability has been proposed within the framework of…
The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally…
For overdamped Langevin systems subjected to weak thermal noise and nonconservative forces, we establish a connection between Freidlin-Wentzell large deviations theory and stochastic thermodynamics. First, we derive a series expansion of…
Macroscopic fluctuations have become an essential tool to understand physics far from equilibrium due to the link between their statistics and nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key information on…
Large deviation theory (LDT) provides a mathematical framework to quantify the probabilities of rare events in stochastic systems. In this study, we applied LDT to model a chemical reaction system and demonstrated that the fluctuation…
Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Tran- sitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible…
We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic…
The precision of reaction-diffusion models for mesoscopic physical systems is limited by fluctuations. To account for this uncertainty, Van Kampen derived a stochastic Langevin-like reaction-diffusion equation that incorporates…
A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction. However its predictions are questionable in…
We prove the emergence of stable fluctuations for reaction-diffusion in random environment with Weibull tails. This completes our work around the quenched to annealed transition phenomenon in this context of reaction diffusion. In [9], we…
Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…
In this review, an outline of the so called Freidlin-Wentzell theory and its recent extensions is given. Broadly, this theory studies the exponential rate at which the probabilities of rare events related to random perturbation of ODE…
This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with $N$ species, $M$ reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical…
As contrast to the Maxwellian distribution, equilibrium distribution of the second kind or turbulent equilibrium is shown to exist under tertiary molecular chaos hypothesis to replace the classical binary chaos by Boltzmann. It is expressed…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…
Chemical reaction networks can undergo nonequilibrium phase transitions upon variation of external control parameters like the chemical potential of a species. We investigate the flux in the associated chemostats that is proportional to the…
Most biochemical reactions in living cells are open systems interacting with environment through chemostats to exchange both energy and materials. At a mesoscopic scale, the number of each species in those biochemical reactions can be…
Comprehensive and predictive simulation of coupled reaction networks has long been a goal of biology and other fields. Currently, metabolic network models that utilize enzyme mass action kinetics have predictive power but are limited in…
Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and…