Computability of Topological Pressure for Shifts of Finite Type with Applications in Statistical Physics

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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 shift dynamical systems of finite type, 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 not computable without further information on the system.