Related papers: Varentropy Decreases Under the Polar Transform
Phase transitions are one of the most interesting natural phenomena. For finite systems, one of the concerns in the topic is how to classify a specific transition as being of first, second, or even of a higher order, according to the…
We introduce novel information-entropic variables -- a Point Divergence Gain (${\Omega}^{(l \rightarrow m)}_\alpha$), a Point Divergence Gain Entropy ($I_\alpha$), and a Point Divergence Gain Entropy Density ($P_\alpha$) -- which are…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
We consider the presence of cosmic string induced density fluctuations in the universe at temperatures below the electroweak phase transition temperature. Resulting temperature fluctuations can restore the electroweak symmetry locally,…
Parity violating physics beyond the standard model of particle physics induces a rotation of the linear polarization of photons. This effect, also known as cosmological birefringence (CB), can be tested with the observations of the cosmic…
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed. Given a tradeoff between $N,P$…
Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A…
We consider the change of entanglement of formation $\Delta E$ produced by a unitary transformation acting on a general (pure or mixed) state $\rho$ describing a system of two qubits. We study numerically the probabilities of obtaining…
We show that spatial quenched disorder affects polar active matter in ways more complex and far-reaching than believed heretofore. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we…
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
Near the melting transition the bending elastic constant, $\kappa$, an emergent property of double-stranded DNA (dsDNA), is shown not to follow the rod-like scaling for small length $N$. The reduction in $\kappa$ with temperature is…
X-ray polarimetry of accreting compact objects has revealed fast time variations in the polarization angle (PA), suggesting that the geometry and/or optical depth of the Comptonization region is changing rapidly. This prompts investigations…
We study polar coding for stochastic processes with memory. For example, a process may be defined by the joint distribution of the input and output of a channel. The memory may be present in the channel, the input, or both. We show that…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
A homogeneous polarized dipolar Bose-Einstein condensate is considered in the presence of weak quenched disorder within mean-field theory at zero temperature. By first solving perturbatively the underlying Gross-Pitaevskii equation and then…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
The notion of polarity between sets, well-known from convex geometry, is a geometric version of the Fourier transform. We exploit this analogy to propose a new simple definition of quantum indeterminacy, using what we call "hbar-polar…
The routine definitions of both entropy, and differential entropy show inconsistencies that make them not reciprocally coherent. We propose a few possible modifications of these quantities so that 1) they no longer show incongruities, 2)…
Transport coefficients and dielectric relaxation in liquids are often treated as distinct manifestations of molecular dynamics. We show that, in polar liquids, orientational dipolar fluctuations generate a substantial contribution to the…
Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…