Related papers: Augmented Transition Path Theory for Sequences of …
This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter",…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
The discovery of transition pathways to unravel distinct reaction mechanisms and, in general, rare events that occur in molecular systems is still a challenge. Recent advances have focused on analyzing the transition path ensemble using the…
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
This article reviews the concepts and methods of variational path sampling. These methods allow computational studies of rare events in systems driven arbitrarily far from equilibrium. Based upon a statistical mechanics of trajectory space…
Yet often neglected, dynamical interdependencies between concomitant contagion processes can alter their intrinsic equilibria and bifurcations. A particular case of interest for disease control is the emergence of explosive transitions in…
Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve…
Quantum causal histories are defined to be causal sets with Hilbert spaces attached to each event and local unitary evolution operators. The reflexivity, antisymmetry, and transitivity properties of a causal set are preserved in the quantum…
The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the "hockey-stick" upward trend of human technological evolution, where an explosion in the number of produced items with…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Transition Path Theory (TPT) provides a rigorous statistical characterization of the ensemble of trajectories connecting directly, i.e., without detours, two disconnected (sets of) states in a Markov chain, a stochastic process that…
The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from the risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular,…