Related papers: Discreteness-induced Transition in Catalytic React…
Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood.…
Fluctuations may govern the fate of an interacting particle system even on the mean-field level. This is demonstrated via a three species cyclic trapping reaction with a large, yet finite number of particles, where the final number of…
Through an appropriate election of the molecular orbital basis, we show analytically that the molecular dissociation occurring in a Heyrovsky reaction can be interpreted as a Quantum Dynamical Phase Transition, i.e., an analytical…
Stochasticity plays important roles in reaction systems. Vector fields of probability flux and velocity characterize time-varying and steady-state properties of these systems, including high probability paths, barriers, checkpoints among…
Quantum mechanical tunneling of atoms is increasingly found to play an important role in many chemical transformations. Experimentally, atom-tunneling can be indirectly detected by temperature-independent rate constants at low temperature…
Many systems that can be described in terms of diffusion-limited `chemical' reactions display non-equilibrium continuous transitions separating active from inactive, absorbing states, where stochastic fluctuations cease entirely. Their…
When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the…
First order phase transitions proceed via nucleation. The rate of nucleation varies exponentially with the free-energy barrier to nucleation, and so is highly sensitive to variations in this barrier. In practice, very few systems are…
This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or…
We introduce the notion of corresponding a chemical reaction network to a split network translation, and use this novel process to extend the scope of existing network-based theory for characterizing the steady state set of mass-action…
Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of "chemical reaction networks", which describes the interactions of molecules in…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo qualitative changes, known as Morse bifurcations, and to exist for a large range of energies, not just immediately above…
We present the first example of a phase transition in a nonequilibrium steady-state that can be argued analytically to be first order. The system of interest is a two-species reaction-diffusion problem whose control parameter is the total…
The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much…
Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross.…
A variety of open quantum networks are currently under intense examination to model energy transport in photosynthetic systems. Here we study the coherent transfer of a quantum excitation over a network incoherently coupled with a…
The freezing/melting transition is at the heart of many natural and industrial processes. In the classical picture, the transition proceeds via the nucleation of the new phase, which has to overcome a barrier associated to the free energy…