Related papers: Continuous time random walk for open systems: Fluc…
Several stochastic processes modeling molecular motors on a linear track are given by random walks (not necessarily Markovian) on quasi 1d lattices and share a common regenerative structure. Analyzing this abstract common structure, we…
Anomalous transport is usually described either by models of continuous time random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE). The asymptotic relation between properly scaled CTRW and fractional diffusion…
Waiting time is an important transport quantity that is complementary to average current and its fluctuation. So far all the studies of waiting time distribution (WTD) are limited to steady state transport (either dc or ac). In this work,…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…
The waiting time distribution (WTD) is a common tool for analysing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete,…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent $\beta(x) \in (0,1)$ varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix…
We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW). The non-trivial incorporation of the reaction process into the CTRW is achieved by…
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in…
Fluctuation theorems impose constraints on the probability of observing negative entropy production in small systems driven out of equilibrium. The range of validity of fluctuation theorems has been extensively tested for transitions…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium…
While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
Expanding media are typical in many different fields, e.g. in Biology and Cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties. Here, we focus on such…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
We study the statistics of first passage times (FPTs) of trajectory observables in both classical and quantum Markov processes. We consider specifically the FPTs of counting observables, that is, the times to reach a certain threshold of a…
In this issue we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different…
The local time in an ensemble of particles measures the amount of time the particles spend in the vicinity of a given point in space. Here we study fluctuations of the empirical time average $R= T^{-1}\int_{0}^{T}\rho\left(x=0,t\right)\,dt$…