We consider two basic types of coarse-graining: the Ehrenfest’s coarsegraining and its extension to a general principle of non-equilibrium thermodynamics, and the coarse-graining based on uncertainty of dynamical models and ε-motions (orbits). Non-technical discussion of basic notions and main coarse-graining theorems are presented: the theorem about entropy overproduction for the Ehrenfest’s c...

A coarse structure $ \mathcal{E}$ on a set $X$ is called finitary if, for each entourage $E\in \mathcal{E}$, there exists natural number $n$ such that E[x]< n $x\in X$. By approximation of \mathcal{E}^\prime$, we mean any \mathcal{E}\subseteq \mathcal{E}^\prime$.If $\mathcal{E}^\prime$ has countable base and $E[x]$ finite X$ then \mathcal{E}^\prime$has cellular the relations linkness subsets...

In experimental work as well as in computational applications for which limited computational resources are available for the numerical calculations a coarse mesh problem frequently appears. In particular, we consider here the problem of numerical integration when the integrand is available only at nodes of a coarse uniform computational grid. Our research is motivated by the coarse mesh proble...