Abstract Gaussian distributions are plentiful in applications dealing uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries probability measures, the resulting geometry on Gaussians is often expressible closed-form under frameworks. In this work, we study entropy-regularized 2-Wasserstein distance, by solutions distance...

1. The Physics of Information 2 2. Thermodynamics 2 2.1. The laws 3 2.2. Free energy 6 3. Statistical mechanics 7 3.1. Definitions and postulates 8 3.2. A simple model system of magnetic spins 9 3.3. The Maxwell-Boltzmann distribution 10 3.4. Free energy revisited 11 3.5. Gibbs entropy 12 4. Nonlinear dynamics 12 4.1. The ergodic hypothesis 13 4.2. Chaos and limits to prediction 14 4.3. Quantif...

We study the evolution of a metric two dimensional black hole under second loop renormalization group fow, RG-2 fow. Since is noncompact (we consider it asymptotically flat) we adapt some proofs for compact case to flat case. found that appearance horizons during related condition parabolicity flow. also show entanglement entropy monotonic generalize results obtained first approximation and dis...

We present an entropy concept measuring phase-space localization in dynamical systems based on time-averaged phase-space densities. This entropy has a direct classical counterpart; its local scaling with ln h ?1=2 is the information dimension of the underlying invariant sets of the classical dynamics. The proposed entropy concept allows to visualize the global phase-space structure of the quant...

The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...

In the second self-creation theory of gravitation and in the general theory of relativity, Bianchi type VI0 cosmological model in the presence of viscous fluid is studied. An exact solution of the field equations is given by considering the cosmological model yields a constant decelerations parameter q=constant and the coefficients of the metric are taken as A(t)=[c1t+c<su...

Contents 10 Quantum Shannon Theory 1 10.1 Shannon for Dummies 2 10.1.1 Shannon entropy and data compression 2 10.1.2 Joint typicality, conditional entropy, and mutual information 6 10.1.3 Distributed source coding 8 10.1.4 The noisy channel coding theorem 9 10.2 Von Neumann Entropy 16 10.2.1 Mathematical properties of H(ρ) 18 10.2.2 Mixing, measurement, and entropy 20 10.2.3 Strong subadditivit...