Related papers: The topological version of free entropy
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
We study the relation between topological string theory and singularity theory using the partition function of $A_{N-1}$ topological string defined by matrix integral of Kontsevich type. Genus expansion of the free energy is considered, and…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
The topological entropy dimension is mainly used to distinguish the zero topological entropy systems. Two types of topological entropy dimensions, the classical entropy dimension and the Pesin entropy dimension, are investigated for…
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…
We review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), where s and t are respective generating…
The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism…
In a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate…
Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…
This is the first installment of a series of papers whose aim is to lay a foundation for homotopy probability theory by establishing its basic principles and practices. The notion of a homotopy probability space is an enrichment of the…
By means of time-dependent density matrix renormalization group calculations we study topological quantum pumping in a strongly interacting system. The system under consideration is described by the Hamiltonian of a one-dimensional extended…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Let $f$ be a $C^2$ diffeomorphism on a compact manifold. Ledrappier and Young introduced entropies along unstable foliations for an ergodic measure $\mu$. We relate those entropies to covering numbers in order to give a new upper bound on…
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…
A detailed comparison is made between the field-theoretic and geometric definitions of topological charge density on the lattice. Their renormalizations with respect to continuum are analysed. The definition of the topological…
This paper presents an information theoretic approach to the concept of intelligence in the computational sense. We introduce a probabilistic framework from which computational intelligence is shown to be an entropy minimizing process at…
Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to…