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The Entropy-Based Quantum Metric [PDF]
Entropy, 2014 The von Neumann entropy S( D ^ ) generates in the space of quantum density matrices D ^ the Riemannian metric ds2 = −d2S( D ^ ), which is physically founded and which characterises the amount of quantum information lost by mixing D ...
Roger Balian
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Metric Entropy of Nonautonomous Dynamical Systems [PDF]
Nonautonomous Dynamical Systems, 2014 We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn; μn) of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1.
Kawan Christoph
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Information Distances versus Entropy Metric [PDF]
Entropy, 2017 Information distance has become an important tool in a wide variety of applications. Various types of information distance have been made over the years.
Bo Hu, Lvqing Bi, Songsong Dai
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Metric Entropy of Homogeneous Spaces [PDF]
Banach Center Publications, 1997 For a (compact) subset $K$ of a metric space and $\varepsilon > 0$, the {\em covering number} $N(K , \varepsilon )$ is defined as the smallest number of balls of radius $\varepsilon$ whose union covers $K$.
Szarek, Stanislaw J.
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(h, Φ)-entropy differential metric [PDF]
Applications of Mathematics, 1997 Considered are monotone functions of integrals of concave or convex functions of probability densities, called generalized entropies. An example is the class of Rényi entropies. For families of parametrized densities, the Hessians along the directions of tangents of the parameter space define differential metrics of a Riemannian geometry.
Menéndez, M. L. +3 more
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De Sitter Entropy in Higher Derivative Theories of Gravity
Universe, 2023 A theorem on higer-order derivative theories of gravity is proved. We find that the de Sitter/anti-de Sitter metric is always a solution of any generally covariant theory of gravity.
An Gong, Kun Liu, Fu-Wen Shu
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Discretising Keyfitz' entropy for studies of actuarial senescence and comparative demography
Methods in Ecology and Evolution, 2023 Keyfitz' entropy is a widely used metric to quantify the shape of the survivorship curve of populations, from plants to animals and microbes. Keyfitz' entropy values 1 correspond to species with a decreasing mortality rate with age (negative senescence),
Charlotte deVries +2 more
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Predicting the Lossless Compression Ratio of Remote Sensing Images With Configurational Entropy
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2021 Compression of remote sensing images is beneficial to both storage and transmission. For lossless compression, the upper and lower limits of compression ratio are defined by Shannon's source coding theorem with Shannon entropy as the metric, which
Xinghua Cheng, Zhilin Li
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Sampling, Metric Entropy, and Dimensionality Reduction [PDF]
SIAM Journal on Mathematical Analysis, 2015 Let $Q$ be a relatively compact subset in a Hilbert space $V$. For a given $\e>0$ let $N(\e,Q)$ be the minimal number of linear measurements, sufficient to reconstruct any $x \in Q$ with the accuracy $\e$. We call $N(\e,Q)$ a sampling $\e$-entropy of $Q$.
Batenkov, Dmitry +2 more
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Duality of metric entropy [PDF]
Annals of Mathematics, 2004 17 p ...
Artstein, S., Milman, V., Szarek, S. J.
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