Related papers: Information entropy of Gegenbauer polynomials of i…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
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…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this…
The so-called Darboux III oscillator is an exactly solvable $N$-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This oscillator can be interpreted as a smooth (super)integrable…
We calculate the entanglement entropy of strongly correlated low-dimensional fermions in metallic, superfluid and antiferromagnetic insulating phases. The entanglement entropy reflects the degrees of freedom available in each phase for…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
The entropy of a classical thermally isolated Hamiltonian system is given by the logarithm of the measure of phase space enclosed by the constant energy hyper-surface, also known as volume entropy. It has been shown that on average the…
Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data…
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an…
Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
This paper investigates the implications from area quantization in Loop Quantum Gravity, particularly focusing on the application of the Landauer principle -- a fundamental thermodynamic concept establishing a connection between information…
This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In…
This paper reveals a conceptually new connection from information theory to approximation theory via quantum algorithms for entropy estimation. Specifically, we provide an information-theoretic lower bound $\Omega(\sqrt{n})$ on the…
The radial expectation values of the probability density of a quantum system in position and momentum spaces allow one to describe numerous physical quantities of the system as well as to find generalized Heisenberg-like uncertainty…
We review the physical foundations of Landauer's Principle, which relates the loss of information from a computational process to an increase in thermodynamic entropy. Despite the long history of the Principle, its fundamental rationale and…
We study different aspects of quantum von Neumann and R\'enyi entanglement entropy of one dimensional long-range harmonic oscillators that can be described by well-defined non-local field theories. We show that the entanglement entropy of…