Let $\Gamma$ be a sofic group, $\Sigma$ be a sofic approximation sequence of
    $\Gamma$ and $X$ be a $\Gamma$-subshift with nonnegative sofic topological
    entropy with respect to $\Sigma$. Further assume that $X$ is a shift of finite
    type, or more generally, that $X$ satisfies the topological Markov property. We
    show that for any sufficiently regular potential $f \colon X \to \mathbb{R}$,
    any translation-invariant Borel probability measure on $X$ which maximizes the
    measure-theoretical sofic pressure of $f$ with respect to $\Sigma$, is a Gibbs
    state with respect to $f$. This extends a classical theorem of Lanford and
    Ruelle, as well as previous generalizations of Moulin Ollagnier, Pinchon,
    Tempelman and others, to the case where the group is sofic.

    As applications of our main result we present a criterion for uniqueness of
    an equilibrium measure, as well as sufficient conditions for having that the
    equilibrium states do not depend upon the chosen sofic approximation sequence.
    We also prove that for any group-shift over a sofic group, the Haar measure is
    the unique measure of maximal sofic entropy for every sofic approximation
    sequence, as long as the homoclinic group is dense.

    On the expository side, we present a short proof of Chung’s variational
    principle for sofic topological pressure.

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