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

Christoph Spandl (Universität der Bundeswehr München, Germany)

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.

Keywords: Type-2 computability, hift dynamical systems, statistical physics, topological pressure

Categories: F.2.1, G.1.2, J.2