In this paper, we establish the entropy-entropy production estimate for ES-BGK model, a generalized version of BGK model Boltzmann equation introduced better approximation in Navier-Stokes limit. Our result improves previous entropy [38] that (1) full range Prandtl parameters −1/2≤ν<1 including critical case ν=−1/2 is covered, and (2) sharper bound obtained. An explicit characterization coeffic...

We study the quantum query complexity of finding a collision for a function f whose outputs are chosen according to a non-uniform distribution D. We derive some upper bounds and lower bounds depending on the min-entropy and the collision-entropy of D. In particular, we improve the previous lower bound in [TTU16] from Ω(2) to Ω(2) where k is the min-entropy of D.

Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. Oneparameter extensions for Shannon entropy have been studied by many researchers [2]. The Rényi entropy [3] and the Tsallis entropy [4] are famous. In the paper [5], the uniqueness theorem for the Tsallis entropy was proven. See also ...

&nbsp;In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

in this paper, the ambiguity of nite state irreducible markov chain trajectories is reminded and is obtained for two state markov chain. i give an applicable example of this concept in president election

A maximum entropy copula is the copula associated with the joint distribution, with prescribed marginal distributions on [0, 1], which maximizes the Tsallis–Havrda–Chavát entropy with q = 2. We find necessary and sufficient conditions for each maximum entropy copula to be a copula in the class introduced in Rodríguez-Lallena and Úbeda-Flores (2004), and we also show that each copula in that cla...

• The entropy is a state function: S = S(state). Furthermore, it is additive; S12 = S1 + S2 for a system with subsystems 1 and 2. • Entropy is unchanged in a reversible state change. That is, S(f) = S(i) and so ∆S = 0. For a reversible state change, entropy increases: S(f) > S(i), and so ∆S > 0. In all cases, ∆S ≥ 0. • When heat is added to a system, then the entropy changes by an amount propor...

For a continuous self-map T of a compact metrizable space with finite topological entropy, the order of accumulation of entropy of T is a countable ordinal that arises in the theory of entropy structure and symbolic extensions. Given any compact manifold M and any countable ordinal α, we construct a continuous, surjective self-map of M having order of accumulation of entropy α. If the dimension...

We explicitly construct a convex entropy function for a hyperbolic system with relaxation. This entropy is deened in the sense of Chen, Levermore and Liu 2], which resembles Boltzman's H-Theorem for kinetic equations. This construction follows the idea of Suliciu's energy function for a rate-type mixed hyperbolic-elliptic system 10]. Such an entropy will be useful in proving the entropy propert...

We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entr...