Markov semigroups of stochastic limit type

In the theory of stochastic limit one deduces, from realistic Hamiltonian of interactions, a natural class of equilibrium and non–equilibrium generators of Markov semi-groups (hence the name stochastic limit type generators).
The two main classes of such generators are:

• 1) Markov generators of weak coupling limit type;
  
• 2) Markov generators of low density limit type.

The Markov generators emerging from this theory have a very special structure which gives, contrarily to the more general but abstract GKSL form, an immediately intuitive picture of the underlying physics, in particular of micro–interactions that build up the whole dynamics.
We believe that the generators of these two classes are the natural candidates for the description of transport phenomena in biological systems and we will discuss their potentialities.