Related papers: Orbital free entropy, revisited
We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…
In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two…
The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a Past Hypothesis, i.e., the assumption of a special (low-entropy) initial state of…
Orbital entropies, pair entropies, and mutual information have become popular tools for analysis of strongly correlated wave functions. They can quantitatively measure how strongly an orbital participates in the electron correlation and…
For an underactuated (simple) Hamiltonian system with two degrees of freedom and one degree of underactuation, a rather general condition that ensures its stabilizability, by means of the existence of a (simple) Lyapunov function, was found…
We study the microstate free entropy of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of their…
Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
Dissipative quantum systems are sometimes phenomenologically described in terms of a non-hermitian hamiltonian $H$, with different left and right eigenvectors forming a bi-orthogonal basis. It is shown that the dynamics of waves in open…
Typically, the entropy of an isolated system in equilibrium is calculated by counting the number of accessible microstates, or in more general cases by using the Gibbs formula. In irreversible processes entropy spontaneously increases and…
In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time…
Under the assumption of the gluing orbit property, equivalent conditions to having zero topological entropy are investigated. In particular, we show that a dynamical system has the gluing orbit property and zero topological entropy if and…
We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.
The present discussion contribution is some remarks concerning and review of the proposal by one of us (C. Balazs) to explain the cosmological constant by a/the principle of entropy. Used without further comment this principle of entropy…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
We define entropy invariants for abstract algebraic structures using an asymptotic Boltzmann formula.
We give an account of the state of the art about black hole entropy in Loop Quantum Gravity. This chapter contains a historical summary and explains how black hole entropy is described by relying on the concept of isolated horizon, with an…