Shift equivalence of measures and the intrinsic structure of shocks in theasymmetric simple exclusion process

We investigate the properties of non-translation-invariant measures, descri bing particle systems on Z, which are asymptotic to different translation i nvariant measures on the left and on the right. Often the structure of the transition region can only be observed from a point of view which is random -in particular, configuration dependent. Two such measures will be called s hift equivalent if they differ only by the choice of such a viewpoint. We i ntroduce certain quantities, called translation sums, which; under some aux iliary conditions, characterize the equivalence classes. Our prime example is the asymmetric simple exclusion process, for which the measures in quest ion describe the microscopic structure of shocks. In this case we compute e xplicitly the translation sums and find that shocks generated in different ways-in particular; via initial conditions in an infinite system or by boun dary conditions in a finite system-are described by shift equivalent measur es. We show also that when the shock in the infinite system is observed fro m the location of a second class par tide, treating this particle either as a first class particle or as an empty site leads to shift equivalent shock measures.