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A sofic approximation to a countable group is a sequence of partial actionson finite sets that asymptotically approximates the action of the group onitself by left-translations. A group is sofic if it admits a soficapproximation. Sofic entropy theory is a generalization of classical entropytheory in dynamics to actions by sofic groups. However, the sofic entropy of anaction may depend on a choice of sofic approximation. All previously knownexamples showing this dependence rely on degenerate behavior. This paperexhibits an explicit example of a mixing subshift of finite type with twodifferent positive sofic entropies. The example is inspired by statisticalphysics literature on 2-colorings of random hyper-graphs.

A topological dynamical system with two different positive sofic entropies