  For any $C^\infty$, area-preserving Anosov diffeomorphism $f$ of a surface,
we show that a suspension flow over $f$ is $C^\infty$-conjugate to a
constant-time suspension flow of a hyperbolic automorphism of the two torus if
and only if the volume measure is the measure with maximal entropy. We also
show that the the metric entropy with respect to the volume measure and the
topological entropy of suspension flow over Anosov diffeomorphisms on torus
achieve all possible values. Our results fit into two programs related to
entropy rigidity and flexibility of Anosov systems.
