Loschmidt's and Zermelo's paradoxes do not exist

Abstract

A strict operational (i.e., informational) analysis of the meaning of preparing a system to realize the paradoxes of Loschmidt or Zermelo is made. Where reversal or recurrence are operationally realizable, no contradiction with the irreversible nature of macroscopic operations occurs. Paradox results either from neglecting irreversible phenomena in the means for preparing a reversed state, or from confusing elements or ensembles, which are meaningful in microstate language but meaningless operationally, with preparable macrostates, whoserepresentation in microstate language is an ensemble whose very definition is incompatible with that of any paradox-generating element or ensemble,