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We investigate properties of non-translation-invariant measures, describingparticle systems on $\bbz$, which are asymptotic to different translationinvariant measures on the left and on the right. Often the structure of thetransition region can only be observed from a point of view which israndom---in particular, configuration dependent. Two such measures will becalled shift equivalent if they differ only by the choice of such a viewpoint.We introduce certain quantities, called translation sums, which, under someauxiliary conditions, characterize the equivalence classes. Our prime exampleis the asymmetric simple exclusion process, for which the measures in questiondescribe the microscopic structure of shocks. In this case we computeexplicitly the translation sums and find that shocks generated in differentways---in particular, via initial conditions in an infinite system or byboundary conditions in a finite system---are described by shift equivalentmeasures. We show also that when the shock in the infinite system is observedfrom the location of a second class particle, treating this particle either asa first class particle or as an empty site leads to shift equivalent shockmeasures.Comment: Plain TeX, 2 figures; derrida@lps.ens.fr, oldstein@math.rutgers.edu,  lebowitz@math.rutgers.edu, speer@math.rutgers.ed

Shift Equivalence of Measures and the Intrinsic Structure of Shocks in the Asymmetric Simple Exclusion Process