Related papers: Evolution of statistical averages: an interdiscipl…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…
We present a stochastic method for the simulation of the time evolution in systems which obey generalized statistics, namely fractional exclusion statistics and Gentile's statistics. The transition rates are derived in the framework of…
Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…
We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman…
We study the time evolution of correlation functions in closed quantum systems for nonequilibrium ensembles of initial conditions. For a scalar quantum field theory we show that generic time-reversal invariant evolutions approach…
We consider the problem of a subnetwork of observed nodes embedded into a larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these hidden states given information about the subnetwork dynamics. The biochemical networks…
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…
Mean field approximation treats only coherent aspects of the evolution of a Bose Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study an analytic model of two counter-propagating atomic…
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…
The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expansion. This expansion assumes a small Knudsen number, and as…
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…
We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under…
We develop a statistical theory of the mean field. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction are random with the…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…
The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done…
Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability…
A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…