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When liquids are cooled sufficiently rapidly below their melting temperature, they may bypass crystalization and, instead, enter a long-lived metastable supercooled state that has long been the focus of intense research. Although they…
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian L\'evy noise. Among these complex phenomena, the most…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
Transition phenomena between thermal noise state and turbulent state observed in a submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely…
We consider the rate of transition for a particle between two metastable states coupled to a thermal environment for various magnitudes of the coupling strength, using the recently proposed infrequent metadynamics approach (Tiwary and…
The Steepest Entropy Ascent approach is considered and applied to few-state systems. When the Hamiltonian of the system is time dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact…
This paper develops a new class of conditional Markov jump processes with regime switching and paths dependence. The key novel feature of the developed process lies on its ability to switch the transition rate as it moves from one state to…
A one-dimensional driven lattice gas with disorder in the particle hopping probabilities is considered. It has previously been shown that in the version of the model with random sequential updating, a phase transition occurs from a low…
Global climate changes are related to the ocean's store of carbon. We study a carbonate system of the upper ocean, which has metastable and oscillatory regimes, under small random fluctuations. We calculate the most probable transition path…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
Singularities in macroscopic systems at discontinuous phase transitions are replaced in finite systems by sharp but continuous changes. Both the energy differences between metastable and stable phases and the energy barriers separating…
Many natural systems exhibit tipping points where changing environmental conditions spark a sudden shift to a new and sometimes quite different state. Global climate change is often associated with the stability of marine carbon stocks. We…
We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates…
In this work, we study the impact of non-Gaussian alpha-stable Levy motion on transitions between metastable equilibrium states (or attractors) in a stochastic Stommel two-box model for thermohaline circulation (THC). By maximizing the…
The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points…