Related papers: Functional evolutions for homogeneous stationary d…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time…
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many research topics such as quantifying species sizes in ecological populations, describing…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
We construct a correlation functions evolution corresponding to the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we prove the…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…
General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General…
Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (noncompact) type space. Conditions are…
We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much…
Combinatorial harmonic analysis techniques are used to develop new functional analysis methods based on Bogoliubov functionals. Concrete applications of the methods are presented, namely, the study of a non-equilibrium stochastic dynamics…
This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian…
The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…
Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are…
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…