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...

Based on the studies on information transmission in discrete multivariable linear time invariant (LTI) system disturbed by stationary noise, relations within entropy rate, mutual information rate and H∞ entropy are discussed in both general control problem and classic tracking problem. For the general control systems, equivalent relations between entropy rate and H ∞ entropy are formulated by u...

A bstract We study upper bounds on the growth of operator entropy S K in growth. Using uncertainty relation, we first prove a dispersion bound rate |∂ t | ≤ 2 b 1 ∆ , where is Lanczos coefficient and variance . However, for irreversible process, this generally turns out to be too loose at long times. further find tighter time limit using universal logarithmic relation between Krylov complexity ...

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 (...