  Let X be a real algebraic surface. The comparison between the volume of real
and complex loci of ample divisors D brings us to define the concordance, which
is a number between 0 and 1. This number equals 1 when the Picard number is 1,
and for some surfaces with a "quite simple" nef cone, e.g. Del Pezzo surfaces.
For abelian surfaces, it is 1/2 or 1, depending on the existence or not of
positive entropy automorphisms on X. In the general case, the existence of such
an automorphism gives an upper bound for the concordance, namely the ratio of
entropies in real and complex loci of X. Moreover the concordance is equal to
this ratio when the Picard number is 2. An interesting consequence of the
inequality is the non-density of the automorphisms in the group of
diffeomorphisms of the real surface X(R), as soon as the concordance is
positive. Finally we show, thanks to this upper bound, that there exist K3
surfaces with arbitrary small concordance, considering a deformation of a
singular surface of tridegree (2,2,2) in the product of three projective lines.
