  Adsorption of a symmetric (AB) random copolymer (RC) onto a symmetric (ab)
random heterogeneous surface (RS) is studied in the annealed approximation by
using a two-dimensional partially directed walk model of the polymer. We show
that in the symmetric case, the expected a posteriori compositions of the RC
and the RS have correct values (corresponding to their a priori probabilities)
and do not change with the temperature, whereas second moments of monomers and
sites distributions in the RC and RS change. This indicates that monomers and
sites do not interconvert but only rearrange in order to provide better
matching between them and, as a result, a stronger adsorption of the RC on the
RS. However, any violation of the system symmetry shifts equilibrium towards
the major component and/or more favorable contacts and leads to interconversion
of monomers and sites.
