Related papers: Phase transition in one-dimensional subshifts
For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive entropy as long as the shift has positive topological…
We present examples of partially hyperbolic and topologically transitive local diffeomorphisms defined as skew products over a horseshoe which exhibit rich phase transitions for the topological pressure. This phase transition follows from a…
The notion of entropy dimension has been introduced to measure the subexponential complexity of zero entropy systems. In this work we present a general construction of a strictly ergodic subshift of topological entropy dimension $\alpha$…
Domino tilings have been studied extensively for both their statistical properties and their dynamical properties. We construct a subshift of finite type using matching rules for several types of dominos. We combine the previous results…
We consider suspension flows with continuous roof function over the full shift $\Sigma$ on a finite alphabet. For any positive entropy subshift of finite type $Y \subset \Sigma$, we explictly construct a roof function such that the…
Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous paper demonstrated how input moments of measures, on a broad…
We provide examples of transitive partially hyperbolic dynamics (specific but paradigmatic examples of homoclinic classes) which blend different types of hyperbolicity in the one-dimensional center direction. These homoclinic classes have…
The family of symmetric one sided subshifts in two symbols given by a sequence $a$ is studied. We analyse some of their topological properties such as transitivity, the specification property and intrinsic ergodicity. It is shown that…
The entanglement properties of the phase transition in a two dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed both, for finite number of particles and thermodynamical limit. We show…
We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…
The most complicated phenomena of equilibrium statistics, phase separations and transitions of various order and critical phenomena, can clearly and sharply be seen even for small systems in the topology of the curvature of the…
We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…
We derive a functional for the entropy contributed by any microscopic degrees of freedom as arising from their measurable pair correlations. Applicable both in and out of equilibrium, this functional yields the maximum entropy which a…
We combine the two classical topological concepts, time-preserving topological factors and synchronizing time-changes of a continuous flow, and explore some of their thermodynamic consequences. Particular focus is put on equilibrium states…
We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…