Entropy production and extraction in dynamical systems and turbulence

In this paper we consider systems deviated from equilibrium by some external factors and discuss the internal entropy production and entropy extraction by the environment. For a system moving away from equilibrium, we express the entropy extraction via a two-point correlation function for any time and any distance from equilibrium. The long-time limit gives the sum of the Lyapunov exponents expressed via the formula of Green-Kubo type. We discuss what is known about the entropy production from deviations away from the equilibrium and back to equilibrium and for turbulent states. In particular, we show that the entropy production is due to the degrees of freedom participating in a direct cascade but not in an inverse cascade.