2008/04/04 by Ian D. Morris, Ian D Morris · 3 citations
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics
paper · doi:10.1088/0951-7715/21/5/005
openalex publication_date 2008/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We prove that for a generic real-valued Hölder continuous function f on a subshift of finite type, every shift-invariant probability measure that maximizes the integral of f must have zero entropy. An immediate corollary is that zero-temperature limits of equilibrium states of certain one-dimensional lattice systems generically have zero entropy. We prove an analogous statement for generic Lipschitz observations of expanding maps of the circle.