Probability, ergodicity, irreversibility and dynamical systems

The problem of irreversibility is difficult and part of this difficulty is due to dealing with the statistical mechanics of a large number of particles. The ergodic theory, founded on the link between thermodynamics and its statistical probability, introduced the ergodic theorem that consists of the equality of microcanonical phase average and the time average of the observables. Moreover, a global approach has been introduced, starting from non-equilibrium thermodynamics and obtaining a general principle of investigation, the principle of maximum entropy generation for the open systems. Here, a general approach to the investigation of irreversible systems and the application of entropy generation to the study of the dynamical systems will be developed.