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Given a countable sofic group $\Gamma$, a finite alphabet $A$, a subshift $X\subseteq A^\Gamma$, and a potential $\phi: X \to \mathbb{R}$, we givesufficient conditions on $X$ and $\phi$ for expressing, in the uniquenessregime, the sofic entropy of the associated Gibbs measure $\mu$ as the limit ofthe Shannon entropies of some suitable finite systems approximating $\Gamma\curvearrowright (X,\mu)$. Next, we prove that if $\mu$ satisfies strongspatial mixing, then the sofic pressure admits a formula in terms of theintegral of a random information function with respect to any$\Gamma$-invariant Borel probability measure with nonnegative sofic entropy. Asa consequence of our results, we provide sufficient conditions on $X$ and$\phi$ for having independence of the sofic approximation for sofic pressureand sofic entropy, and for having locality of pressure in some relevantfamilies of systems, among other applications. These results complement andunify those of Marcus and Pavlov (2015), Alpeev (2017), and Austin and Podder(2018).

Kieffer-Pinsker type formulas for Gibbs measures on sofic groups