Why irreversibility is not a sufficient condition for ergodicity.
Khinchin's theorem of ergodicity is examined by means of linear response theory. The resulting ergodic condition shows that, contrary to the theorem, irreversibility is not a sufficient condition for ergodicity. By the recurrence relations method, we prove that irreversibility is broader in scope than ergodicity, showing why it can only be a necessary condition for ergodicity.
Department of Physics and Astronomy, University of Georgia, Athens, GA 30602, USA. MHLee@uga.edu
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