We show that the Voiculescu-Brown entropy of a noncommutative toral automorphism arising from a matrix S ∈ GL(d,Z) is at least half the value of the topological entropy of the corresponding classical toral automorphism. We also obtain some information concerning the positivity of local Voiculescu-Brown entropy with respect to single unitaries. In particular we show that if S has no roots of uni...

We show that the Voiculescu-Brown entropy of a noncommutative toral automorphism arising from a matrix S ∈ GL(d,Z) is at least half the value of the topological entropy of the corresponding classical toral automorphism. We also obtain some information concerning the positivity of local Voiculescu-Brown entropy with respect to single unitaries. In particular we show that if S has no roots of uni...

Recently, the problem of privacy amplification with an active adversary has received a lot of attention. Given a shared n-bit weak random source X with min-entropy k and a security parameter s, the main goal is to construct an explicit 2-round privacy amplification protocol that achieves entropy loss O(s). Dodis and Wichs [DW09] showed that optimal protocols can be achieved by constructing expl...

Let A be a subset of a type p Banach space E, 1 < p ≤ 2, such that its entropy numbers satisfy ( εn(A) ) n ∈ `q,s for some q, s ∈ (0,∞). We show ( en(acoA) ) n ∈ `r,s for the dyadic entropy numbers of the absolutely convex hull acoA of A, where r is defined by 1/r = 1/p′+1/q. Furthermore, we show for slowly decreasing entropy numbers that ( en(A) ) n ∈ `q,s implies ( en(acoA) ) n ∈ `p′,s for al...

High-entropy (H-E) alloys, bulk metallic glasses (BMGs) and high-entropy BMGs (HE-BMGs) were statistically analyzed with the help of a database of ternary amorphous alloys. Thermodynamic quantities corresponding to heat of mixing and atomic size differences were calculated as a function of composition of the multicomponent alloys. Actual calculations were performed for configurational entropy (...

The change in entropy, S , associated with the quasi-static absorption of a particle of energy ε by a Schwarzschild black hole (ScBH) is approximately (ε/T )− s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. Motivated by the statistical interpretation of entropy, it is proposed here that the absorption should be suppressed, but not forbidden, when S ...

This study discusses the application of Taguchi method in assessing minimum entropy generation and maximum heat transfer rate for natural convection in an enclosure embedded with isothermal cylinder. The simulations were planned based on Taguchi’s L25 orthogonal array with each trial performed under different conditions of position and aspect ratio (AR) of the cylinder. The thermal lattice Bolt...

Computational notions of entropy have recently found many applications, including leakageresilient cryptography, deterministic encryption or memory delegation. The two main types of results which make computational notions so useful are (1) Chain rules, which quantify by how much the computational entropy of a variable decreases if conditioned on some other variable (2) Transformations, which q...

OBJECTIVE To identify the entropy levels that would correspond to bispectral index (BIS) levels in general anesthesia (GA) induction in patients who will undergo elective lumbar disc surgery (LDS). METHODS Thirty cases who underwent LDS under GA were included in our study after obtaining patient consent and approval of the Ethics Committee of Afyon Kocatepe University Medical School, Afyonkar...