Ergodicity in simple and not so simple systems and Kuboʹs condition

The ergodic hypothesis is approached from the side of time averaging to ascertain regions of its validity. A necessary and sufficient condition is formulated in terms of certain infinite products and tested in models of nn coupled harmonic oscillators. The validity of the hypothesis requires energy delocalizability, indicated by the existence of coherent translation modes. Kuboʹs condition is re-examined to see the origin of its limitations.