Computability of Topological Pressure for Sofic Shifts with Applications in Statistical Physics

Abstract: 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.