Related papers: A geometric approach to Voiculescu-Brown entropy
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
We consider C*-algebras of finite higher-rank graphs along with their rotational action. We show how the entropy theory of product systems with finite frames applies to identify the phase transitions of the dynamics. We compute the positive…
For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak-$*$ topology has infinite topological mean dimension. We also estimate the rate of…
We examine the relation between topological entropy, invertability, and prediction in topological dynamics. We show that topological determinism in the sense of Kamisky Siemaszko and Szymaski imposes no restriction on invariant measures…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
The evolution of entropy is derived with respect to dynamical systems. For a stochastic system, its relative entropy $D$ evolves in accordance with the second law of thermodynamics; its absolute entropy $H$ may also be so, provided that the…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
In this paper we study two entropic dynamical models from the viewpoint of information geometry. We study the geometry structures of the associated statistical manifolds. In order to analyse the character of the instability of the systems,…
We give entropy estimates for two canonical non commutative shifts on $C^*$-algebras associated to some topological graphs $E=(E^0,E^1,s,r)$, defined using a basis of the corresponding Hilbert bimodule $H(E)$. We compare their entropies…
In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum…
We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact…
In this paper, we mainly revisit a nice theory for topological entropy of weakly equivalent flows, which was originally investigated by Ohno in 1980. We will develop a new approach, being more straightforward and elementary than the…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…
We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…
A recent article uncovered a surprising dynamical mechanism at work within the (vacuum) Einstein `flow' that strongly suggests that many closed 3-manifolds that do not admit a locally homogeneous and isotropic metric \textit{at all} will…
Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic…