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We show that for any invariant measure $\mu$ on a free group shift system,there are two numbers $h^\flat \leq h^\sharp$ which in some sense are thetypical upper and lower sofic entropy values. We also give a condition underwhich $h^\flat = h^\sharp = \mathrm{f}(\mu)$, where $\mathrm{f}$ is theannealed entropy (also called the f invariant). This can be used to computetypical local limits of finitary Gibbs states over sequences of random regulargraphs. As examples, we work out typical local limits of the Ising and Pottsmodels.  We also show that, for Markov chains, the Kesten--Stigum second-eigenvaluereconstruction criterion actually implies there are no good models over atypical sofic approximation (i.e. $h^\sharp = -\infty$). In particular, we havean exact value for the typical entropy $h^\flat = h^\sharp$ of thefree-boundary Ising state: it is equal to the annealed entropy $\mathrm{f}$ forinteraction strengths up to the reconstruction threshold, after which it dropsabruptly to $-\infty$.

Typical sofic entropy and local limits for free group shift systems