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We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
Causal ordering of key events in the cell cycle is essential for proper functioning of an organism. Yet, it remains a mystery how a specific temporal program of events is maintained despite ineluctable stochasticity in the biochemical…
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…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
We consider open quantum walks on a graph, and consider the random variables defined as the passage time and number of visits to a given point of the graph. We study in particular the probability that the passage time is finite, the…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the…
A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic…
We discuss the stochastic interpretation of a control system determined by a system of differential equations on a tree. For example, such a system on a finite tree arises after replacing the coefficients of the equation on an interval with…
Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
The escape mechanism of the four hill potential is explored. A thorough numerical investigation takes place in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space in…
We consider noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
The observable behavior of a complex system reflects the mechanisms governing the internal interactions between the system's components and the effect of external perturbations. Here we show that by capturing the simultaneous activity of…