  In this paper, we prove that for a $C^\infty$-generic Finsler (symmetric
Finsler and Riemannian) metric on a closed surface $\Sigma$, there exists a
sequence of (nondegenerate) closed geodesics which are equidistributed on
$\Sigma$. The proof is based on the volume property of the spectral invariants
in embedded contact homology theory by Cristofaro-Gardiner, Hutchings, Ramos
and some transversality arguments, which are inspired by the equidistribution
result of Irie for three-dimensional Reeb flows and the analogous result of
Marques, Neves and Song for embedded minimal hypersurfaces.
