These constructions lead to obstructions in using subshifts in applications to properties of the prime numbers and in finding a measurable version of the complexity gap that arises for shifts of sublinear complexity. With a different construction, we show that there exists a minimal subshift with an ergodic measure such that the liminf of the slow entropy grows slower than any given rate tending to infinitely but the limsup grows faster than any other rate majorizing this one yet still growing subexponentially. By constructing minimal subshifts whose block complexity is arbitrarily close to linear but have uncountably many ergodic measures, we show that this behavior fails as soon as the block complexity is superlinear. Section3uses notions from computability theory (also called recursion theory). See Lind and Marcus 5 for an introduction to subshifts. These constructions lead to obstructions in using subshifts in applications to properties of the prime numbers and in finding a measurable version of the complexity gap that arises for shifts of sublinear complexity.ĪB - A subshift with linear block complexity has at most countably many ergodic measures, and we continue the study of the relation between such complexity and the invariant measures. S nN of all sequences that avoid Sis called a subshift (or a shift space) and the elements of Sare called forbidden words. First, we find the classical stochastic processes corresponding to non-Markovian quantum state diffusion and non-Markovian quantum jumps in projective Hilbert space. N2 - A subshift with linear block complexity has at most countably many ergodic measures, and we continue the study of the relation between such complexity and the invariant measures. We solve two long-standing problems for stochastic descriptions of open quantum system dynamics. © 2020, The Hebrew University of Jerusalem. The second author was partially supported by NSF grant 1800544. space and a topologically transitive homeomorphism (subshift of finite. T1 - Realizing ergodic properties in zero entropy subshifts for dissipative reversible transitive Anosov diffeomorphisms is extended to the.
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