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

: 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. Key Words: shift dynamical systems, topological pressure, Type-2 computability, statistical physics

• Type: Journal
• Year: 2008
• Where: JUCS
• Authors: Christoph Spandl
• Keywords: Dynamical Systems, JUCS 2008, Shift Dynamical Systems, Topological Pressure