Related papers: The entropic central limit theorem for stochastic …
In this paper we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems \begin{equation*} H=h(y)+f(x,y,t), \end{equation*} where $y\in D\subseteq\mathbb{R}^n$ with $D$ being a closed bounded domain,…
We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians - those that are related to quadratic forms of Fermi operators - between the first N spins and the rest of the system in the…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…
The information entropy budget and the rate of information transfer between variables is studied in the context of a nonlinear reduced-order atmospheric model. The key ingredients of the dynamics are present in this model, namely the…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
The realization of Hawking radiation in optical analogs has historically focused on kinematic observables, such as the effective temperature determined by the horizon's surface gravity. A complete thermodynamic description, however,…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
We elucidate how Chern and topological insulators fulfill an area law for the entanglement entropy. By explicit construction of a family of lattice Hamiltonians, we are able to demonstrate that the area law contribution can be tuned to an…
We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones.…
Strong and general entropic and geometric Heisenberg limits are obtained, for estimates of multiparameter unitary displacements in quantum metrology, such as the estimation of a magnetic field from the induced rotation of a probe state in…
This article establishes an asymptotic theory for volatility estimation in an infinite-dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
It is known that, if a point in $R^n$ is driven by a bounded below potential $V$, whose gradient is always in a closed convex cone which contains no lines, then the velocity has a finite limit as time goes to $+\infty$. The components of…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change…