Corresponding author: Christoph Spandl (

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The topological pressure of dynamical systems theory is examined from a computability theoretic point of view. It is shown that for sofic shift dynamical systems, the topological pressure is a computable function. This result is applied to a certain class of one dimensional spin systems in statistical physics. As a consequence, the specific free energy of these spin systems is computable. Finally, phase transitions of these systems are considered. It turns out that the critical temperature is recursively approximable.