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We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…
The fluctuation-dissipation theorem is a hallmark of equilibrium system that stem from their time-reversal symmetry. In many non-equilibrium systems, in particular active ones, extensions and explicit violations of this theorem are used to…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…
In this paper we presented an overview on our works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type's…
Static disorder in a 3D crystal degrades the ideal ballistic dynamics until it produces a localized regime. This Metal-Insulator Transition is often preceded by coherent diffusion. By studying three paradigmatic 1D models, namely the…
Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently…
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and Neumann type boundary conditions. Our results concern various…
We introduce axiomatically a complete thermodynamic formalism for a single macromolecule, either with or without detailed balance, in an isothermal ambient fluid based on its stochastic dynamics. With detailed balance, the novel theory…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
We consider the potentially degenerate haptotaxis system \begin{equation*} \left\{ \begin{aligned} u_t &= \nabla \cdot (\mathbb{D} \nabla u + u \nabla \cdot \mathbb{D}) - \chi \nabla \cdot (u\mathbb{D}\nabla w) + \mu u(1-u^{r- 1}), \\ w_t…
Quantum decoherence is of primary importance for relaxation to an equilibrium distribution and, accordingly, for equilibrium processes. We demonstrate how coherence breaking implies evolution to a microcanonical distribution…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…
We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is…
Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic…
We discuss the effective diffusion constant $D_{{\it eff}}$ for stochastic processes with spatially-dependent noise. Starting from a stochastic process given by a Langevin equation, different drift-diffusion equations can be derived…
A self-consistent and universal description of friction and diffusion for Brownian particles (grains) in different systems, as a gas with Boltzmann collisions, dusty plasma with ion absorption by grains, and for active particles (e.g.,…