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We discuss the well known Einstein and the Kubo Fluctuation Dissipation Relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multi-variate linear Langevin model, which…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics…
The life of a cell is governed by highly dynamical microscopic processes. Two notable examples are the diffusion of membrane receptors and the kinetics of transcription factors governing the rates of gene expression. Different fluorescence…
The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals T as T goes to infinity and it is a generalization of the fluctuation--dissipation theorem to far from equilibrium…
We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…
For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation…
We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response…
For more than ten years now, many efforts have been done to identify and characterize nature of obstructed diffusion in model and cellular lipid membranes. Amongst all the techniques developed for this purpose, FCS, by means of…
A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or…
Nature presents multiple intriguing examples of processes which proceed at high precision and regularity. This remarkable stability is frequently counter to modelers' experience with the inherent stochasticity of chemical reactions in the…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…
In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…
We adapt Fluorescence Correlation spectroscopy (FCS) formalism to the studies of the dynamics of semi-flexible polymers and derive expressions relating FCS correlation function to the longitudinal and transverse mean square displacements of…
It is shown that the work fluctuations and work distribution functions are fundamentally different in systems with short-range versus long-range correlations. The two cases considered with long- range correlations are magnetic work…