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We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the…

In this paper, we consider a dynamical system on the Riemann sphere that evolves through a set-valued map, namely a holomorphic correspondence. Analogous to the investigation of the dynamics effected by a continuous map defined on a compact…

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological…

We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…

By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner…

A `symbolic dynamical system' is a continuous transformation F:X-->X of a closed perfect subset X of A^V, where A is a finite set and V is countable. (Examples include subshifts, odometers, cellular automata, and automaton networks.) The…

This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of…

We study two variations of Bowen's definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces. We prove that these definitions reduce to…

Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…

The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…

In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way…

The $f$-invariant is a notion of entropy for probability-measure-preserving actions of free groups. We show it is invariant under bounded orbit-equivalence.

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…

In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study…

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…

We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological…

The goal of this paper is to define and investigate those topological pressures, which is an extension of topological entropy presented by Feng and Huang [13], of continuous transformations. This study reveals the similarity between many…

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…

We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to…